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2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project. This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

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2.29 Numerical Fluid Dynamics (MIT) 2.29 Numerical Fluid Dynamics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs). This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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2.29 Numerical Fluid Mechanics (MIT) 2.29 Numerical Fluid Mechanics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the

Subjects

errors | errors | condition numbers and roots of equations | condition numbers and roots of equations | Navier-Stokes | Navier-Stokes | direct and iterative methods for linear systems | direct and iterative methods for linear systems | finite differences for elliptic | finite differences for elliptic | parabolic and hyperbolic equations | parabolic and hyperbolic equations | Fourier decomposition | Fourier decomposition | error analysis | error analysis | and stability | and stability | high-order and compact finite-differences | high-order and compact finite-differences | finite volume methods | finite volume methods | time marching methods | time marching methods | Navier-Stokes solvers | Navier-Stokes solvers | grid generation | grid generation | finite volumes on complex geometries | finite volumes on complex geometries | finite element methods | finite element methods | spectral methods | spectral methods | boundary element and panel methods | boundary element and panel methods | turbulent flows | turbulent flows | boundary layers | boundary layers | Lagrangian Coherent Structures | Lagrangian Coherent Structures

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB&#1 This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB&#1

Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derviative | substantial derviative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics | Incompressible | Incompressible

License

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.100 Aerodynamics (MIT) 16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.

Subjects

aerodynamics | aerodynamics | airflow | airflow | air | air | body | body | aircraft | aircraft | aerodynamic modes | aerodynamic modes | aero | aero | forces | forces | flow | flow | computational | computational | CFD | CFD | aerodynamic analysis | aerodynamic analysis | lift | lift | drag | drag | potential flows | potential flows | imcompressible | imcompressible | supersonic | supersonic | subsonic | subsonic | panel method | panel method | vortex lattice method | vortex lattice method | boudary layer | boudary layer | transition | transition | turbulence | turbulence | inviscid | inviscid | viscous | viscous | euler | euler | navier-stokes | navier-stokes | wind tunnel | wind tunnel | flow similarity | flow similarity | non-dimensional | non-dimensional | mach number | mach number | reynolds number | reynolds number | integral momentum | integral momentum | airfoil | airfoil | wing | wing | stall | stall | friction drag | friction drag | induced drag | induced drag | wave drag | wave drag | pressure drag | pressure drag | fluid element | fluid element | shear strain | shear strain | normal strain | normal strain | vorticity | vorticity | divergence | divergence | substantial derivative | substantial derivative | laminar | laminar | displacement thickness | displacement thickness | momentum thickness | momentum thickness | skin friction | skin friction | separation | separation | velocity profile | velocity profile | 2-d panel | 2-d panel | 3-d vortex | 3-d vortex | thin airfoil | thin airfoil | lifting line | lifting line | aspect ratio | aspect ratio | twist | twist | camber | camber | wing loading | wing loading | roll moments | roll moments | finite volume approximation | finite volume approximation | shocks | shocks | expansion fans | expansion fans | shock-expansion theory | shock-expansion theory | transonic | transonic | critical mach number | critical mach number | wing sweep | wing sweep | Kutta condition | Kutta condition | team project | team project | blended-wing-body | blended-wing-body | computational fluid dynamics | computational fluid dynamics

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT) 16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT)

Description

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations). A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Subjects

numerical methods | numerical methods | differential equations | differential equations | linear | linear | nonlinear | nonlinear | elliptic | elliptic | parabolic | parabolic | hyperbolic | hyperbolic | partial differential equations | partial differential equations | integral equations | integral equations | mathematical formulations | mathematical formulations | mathematics | mathematics | finite difference | finite difference | finite volume | finite volume | discretisation | discretisation | finite element | finite element | boundary element | boundary element | iteration | iteration | 16.920 | 16.920 | 2.097 | 2.097 | 6.339 | 6.339

License

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18.336 Numerical Methods for Partial Differential Equations (MIT) 18.336 Numerical Methods for Partial Differential Equations (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods. This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

advection equation | advection equation | heat equation | heat equation | wave equation | wave equation | Airy equation | Airy equation | convection-diffusion problems | convection-diffusion problems | KdV equation | KdV equation | hyperbolic conservation laws | hyperbolic conservation laws | Poisson equation | Poisson equation | Stokes problem | Stokes problem | Navier-Stokes equations | Navier-Stokes equations | interface problems | interface problems | consistency | consistency | stability | stability | convergence | convergence | Lax equivalence theorem | Lax equivalence theorem | error analysis | error analysis | Fourier approaches | Fourier approaches | staggered grids | staggered grids | shocks | shocks | front propagation | front propagation | preconditioning | preconditioning | multigrid | multigrid | Krylov spaces | Krylov spaces | saddle point problems | saddle point problems | finite differences | finite differences | finite volumes | finite volumes | finite elements | finite elements | ENO/WENO | ENO/WENO | spectral methods | spectral methods | projection approaches for incompressible ows | projection approaches for incompressible ows | level set methods | level set methods | particle methods | particle methods | direct and iterative methods | direct and iterative methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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2.29 Numerical Fluid Mechanics (MIT)

Description

This course will provide students with an introduction to numerical methods and MATLAB®. Topics covered throughout the course will include: errors, condition numbers and roots of equations; Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis, and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; Lagrangian Coherent Structures. Subject includes a final research project.

Subjects

errors | condition numbers and roots of equations | Navier-Stokes | direct and iterative methods for linear systems | finite differences for elliptic | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | finite volume methods | time marching methods | Navier-Stokes solvers | grid generation | finite volumes on complex geometries | finite element methods | spectral methods | boundary element and panel methods | turbulent flows | boundary layers | Lagrangian Coherent Structures

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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2.29 Numerical Fluid Mechanics (MIT)

Description

This course is an introduction to numerical methods and MATLAB®: Errors, condition numbers and roots of equations. Topics covered include Navier-Stokes; direct and iterative methods for linear systems; finite differences for elliptic, parabolic and hyperbolic equations; Fourier decomposition, error analysis and stability; high-order and compact finite-differences; finite volume methods; time marching methods; Navier-Stokes solvers; grid generation; finite volumes on complex geometries; finite element methods; spectral methods; boundary element and panel methods; turbulent flows; boundary layers; and Lagrangian coherent structures (LCSs).Prof. Pierre Lermusiaux is very grateful to the teaching assistants Dr. Matt Ueckermann, Dr. Tapovan Lolla, Mr. Jing Lin, and Mr. Arpit Agarwal for the

Subjects

errors | condition numbers and roots of equations | Navier-Stokes | direct and iterative methods for linear systems | finite differences for elliptic | parabolic and hyperbolic equations | Fourier decomposition | error analysis | and stability | high-order and compact finite-differences | finite volume methods | time marching methods | Navier-Stokes solvers | grid generation | finite volumes on complex geometries | finite element methods | spectral methods | boundary element and panel methods | turbulent flows | boundary layers | Lagrangian Coherent Structures

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT) 16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints. This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | numerical integration | ODEs | ODEs | ordinary differential equations | ordinary differential equations | finite difference | finite difference | finite volume | finite volume | finite element | finite element | discretization | discretization | PDEs | PDEs | partial differential equations | partial differential equations | numerical linear algebra | numerical linear algebra | probabilistic methods | probabilistic methods | optimization | optimization | omputational methods | omputational methods | aerospace engineering | aerospace engineering | computational methods | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem. Technical RequirementsFile decompression software, such as Winzip® or StuffIt®, is required to open the .tar files found on this course site. MATLAB&#1

Subjects

aerodynamics | airflow | air | body | aircraft | aerodynamic modes | aero | forces | flow | computational | CFD | aerodynamic analysis | lift | drag | potential flows | imcompressible | supersonic | subsonic | panel method | vortex lattice method | boudary layer | transition | turbulence | inviscid | viscous | euler | navier-stokes | wind tunnel | flow similarity | non-dimensional | mach number | reynolds number | integral momentum | airfoil | wing | stall | friction drag | induced drag | wave drag | pressure drag | fluid element | shear strain | normal strain | vorticity | divergence | substantial derviative | laminar | displacement thickness | momentum thickness | skin friction | separation | velocity profile | 2-d panel | 3-d vortex | thin airfoil | lifting line | aspect ratio | twist | camber | wing loading | roll moments | finite volume approximation | shocks | expansion fans | shock-expansion theory | transonic | critical mach number | wing sweep | Kutta condition | team project | blended-wing-body | computational fluid dynamics | Incompressible

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.Technical RequirementsMATLAB® software is required to run the .m and .mat files found on this course site.MATLAB® is a trademark of The MathWorks, Inc.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | computational methods

License

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16.100 Aerodynamics (MIT)

Description

This course extends fluid mechanic concepts from Unified Engineering to the aerodynamic performance of wings and bodies in sub/supersonic regimes. 16.100 generally has four components: subsonic potential flows, including source/vortex panel methods; viscous flows, including laminar and turbulent boundary layers; aerodynamics of airfoils and wings, including thin airfoil theory, lifting line theory, and panel method/interacting boundary layer methods; and supersonic and hypersonic airfoil theory. Course material varies each year depending upon the focus of the design problem.

Subjects

aerodynamics | airflow | air | body | aircraft | aerodynamic modes | aero | forces | flow | computational | CFD | aerodynamic analysis | lift | drag | potential flows | imcompressible | supersonic | subsonic | panel method | vortex lattice method | boudary layer | transition | turbulence | inviscid | viscous | euler | navier-stokes | wind tunnel | flow similarity | non-dimensional | mach number | reynolds number | integral momentum | airfoil | wing | stall | friction drag | induced drag | wave drag | pressure drag | fluid element | shear strain | normal strain | vorticity | divergence | substantial derivative | laminar | displacement thickness | momentum thickness | skin friction | separation | velocity profile | 2-d panel | 3-d vortex | thin airfoil | lifting line | aspect ratio | twist | camber | wing loading | roll moments | finite volume approximation | shocks | expansion fans | shock-expansion theory | transonic | critical mach number | wing sweep | Kutta condition | team project | blended-wing-body | computational fluid dynamics

License

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16.920J Numerical Methods for Partial Differential Equations (SMA 5212) (MIT)

Description

A presentation of the fundamentals of modern numerical techniques for a wide range of linear and nonlinear elliptic, parabolic and hyperbolic partial differential equations and integral equations central to a wide variety of applications in science, engineering, and other fields. Topics include: Mathematical Formulations; Finite Difference and Finite Volume Discretizations; Finite Element Discretizations; Boundary Element Discretizations; Direct and Iterative Solution Methods.This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5212 (Numerical Methods for Partial Differential Equations).

Subjects

numerical methods | differential equations | linear | nonlinear | elliptic | parabolic | hyperbolic | partial differential equations | integral equations | mathematical formulations | mathematics | finite difference | finite volume | discretisation | finite element | boundary element | iteration | 16.920 | 2.097 | 6.339

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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18.336 Numerical Methods for Partial Differential Equations (MIT)

Description

This graduate-level course is an advanced introduction to applications and theory of numerical methods for solution of differential equations. In particular, the course focuses on physically-arising partial differential equations, with emphasis on the fundamental ideas underlying various methods.

Subjects

advection equation | heat equation | wave equation | Airy equation | convection-diffusion problems | KdV equation | hyperbolic conservation laws | Poisson equation | Stokes problem | Navier-Stokes equations | interface problems | consistency | stability | convergence | Lax equivalence theorem | error analysis | Fourier approaches | staggered grids | shocks | front propagation | preconditioning | multigrid | Krylov spaces | saddle point problems | finite differences | finite volumes | finite elements | ENO/WENO | spectral methods | projection approaches for incompressible ows | level set methods | particle methods | direct and iterative methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.90 Computational Methods in Aerospace Engineering (MIT)

Description

This course provides an introduction to numerical methods and computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques covered include numerical integration of systems of ordinary differential equations; numerical discretization of partial differential equations; and probabilistic methods for quantifying the impact of variability. Specific emphasis is given to finite volume methods in fluid mechanics, and finite element methods in structural mechanics.Acknowledgement: Prof. David Darmofal taught this course in prior years, and created some of the materials found in this OCW site.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | computational methods | aerospace engineering | Monte Carlo | Fourier stability analysis | Matrix stability analysis | Runge-Kutta | convergence | accuracy | stiffness | weighted residual | statistical sampling | sensitivity analysis

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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16.901 Computational Methods in Aerospace Engineering (MIT)

Description

This course serves as an introduction to computational techniques arising in aerospace engineering. Applications are drawn from aerospace structures, aerodynamics, dynamics and control, and aerospace systems. Techniques include: numerical integration of systems of ordinary differential equations; finite-difference, finite-volume, and finite-element discretization of partial differential equations; numerical linear algebra; eigenvalue problems; and optimization with constraints.

Subjects

numerical integration | ODEs | ordinary differential equations | finite difference | finite volume | finite element | discretization | PDEs | partial differential equations | numerical linear algebra | probabilistic methods | optimization | omputational methods | aerospace engineering | computational methods

License

Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm

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