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# <span style="color:rgb(213,80,0)">Computational Fluid Dynamics Course Module</span>
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[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module)
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[![View on File Exchange](https://www.mathworks.com/matlabcentral/images/matlab-file-exchange.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics) or [![Open in MATLAB Online](https://www.mathworks.com/images/responsive/global/open-in-matlab-online.svg)](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics)
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**Curriculum Module**
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**On MATLAB Online:**
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Use the [<img src="Images/OpenInMO.png" width="136" alt="OpenInMO.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module) link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see Overview.mlx laying out the contents of the repository.
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Use the [<img src="Images/OpenInMO.png" width="136" alt="OpenInMO.png">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics) link to download the module. You will be prompted to log in or create a MathWorks account. The project will be loaded, and you will see Overview.mlx laying out the contents of the repository.
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**On Desktop:**
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| **Topic** <br> | **Summary** <br> | **Learning Objectives** <br> | **Mode** <br> |
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| **Intro to finite difference methods and numerical errors** in <br> [**numericalErrors.mlx** ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/numericalErrors.mlx) <br> [<img src="Images/image1.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/numericalErrors.mlx) <br> | This script introduces the motivation behind solving partial differential equations, using finite difference methods to solve them, and the numerical errors behind computing. <br> | \* Understand basic sources of error in computing <br> | Code Hidden <br> |
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| **Solving parabolic equations** in [**parabolicEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/parabolicEquations.mlx) <br> [<img src="Images/image2.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/parabolicEquations.mlx) <br> | Introduction to solving parabolic partial differential equations.<br> | \* Determine local truncation error <br> \* How to perform stability analysis and fine stability criteria <br> \* Learn to test if the solution is converging <br>| Code Visible <br> |
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| **Solving hyperbolic equations** in [**hyperbolicEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/hyperbolicEquations.mlx) <br> [<img src="Images/hyperbolic.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/hyperbolicEquations.mlx) <br> | Learn about specific methods for solving hyperbolic equations. <br> | \* Understand the direction of information travel and which numerical schemes are needed <br> \* The stability criteria <br> \* Dispersion <br> | Code Visible <br> |
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| **Solving elliptic equations** in [**ellipticEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/ellipticEquations.mlx) <br> [<img src="Images/elliptic.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FiniteDifferenceMethods/ellipticEquations.mlx) <br> | Learn how to solve boundary value problems. <br> | \* Identify thermal sources, sinks, and reservoirs <br> \* Learn how to use iterative methods to solve solutions for steady state problems. <br> | Code Visible <br> |
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| **Solving incompressible Navier-Stokes equations** in [**flowSolver_teachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=NavierStokes/flowSolver_teachingModule.mlx) <br> [<img src="Images/streamlines_Re_1000.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=NavierStokes/flowSolver_teachingModule.mlx) <br> | Learn how to solve the 2D incompressible NSE and build the entire solver. <br> | \* Learn how to setup a staggered grid of variables <br> \* How to setup velocity and pressure boundary conditions <br> \* Learn how to solve the x and y momentum equations <br> \* Two step projection method for divergence free velocity field <br> | Code Visible <br> |
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| **Building an interface advection scheme (SLIC)** in [**interfaceAdvectionTeachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=InterfaceAdvection/interfaceAdvection_teachingModule.mlx) <br> [<img src="Images/interface.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=InterfaceAdvection/interfaceAdvection_teachingModule.mlx) <br> | Learn how to build an interface advection scheme using the Volume-of-Fluid method and the SLIC geometric reconstruction method. <br> | \* Simple line interface construction <br> \* Flux calculation <br> | Code Visible <br> |
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| **Fluid structure interaction** in [**FSI_teachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FluidStructureInteraction/FSI_teachingModule.mlx) <br> [<img src="Images/fsi.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics-Course-Module&file=FluidStructureInteraction/FSI_teachingModule.mlx) <br> | Learn how to introduce an immersed structure into the fluid domain. <br> | \* Classic immersed boundary method for elastic structures. <br> \* Direct forcing fictitious domain method for rigid bodies. <br> | Code Visible <br>
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| **Intro to finite difference methods and numerical errors** in <br> [**numericalErrors.mlx** ](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/numericalErrors.mlx) <br> [<img src="Images/image1.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/numericalErrors.mlx) <br> | This script introduces the motivation behind solving partial differential equations, using finite difference methods to solve them, and the numerical errors behind computing. <br> | \* Understand basic sources of error in computing <br> | Code Hidden <br> |
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| **Solving parabolic equations** in [**parabolicEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/parabolicEquations.mlx) <br> [<img src="Images/image2.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/parabolicEquations.mlx) <br> | Introduction to solving parabolic partial differential equations.<br> | \* Determine local truncation error <br> \* How to perform stability analysis and fine stability criteria <br> \* Learn to test if the solution is converging <br>| Code Visible <br> |
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| **Solving hyperbolic equations** in [**hyperbolicEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/hyperbolicEquations.mlx) <br> [<img src="Images/hyperbolic.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/hyperbolicEquations.mlx) <br> | Learn about specific methods for solving hyperbolic equations. <br> | \* Understand the direction of information travel and which numerical schemes are needed <br> \* The stability criteria <br> \* Dispersion <br> | Code Visible <br> |
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| **Solving elliptic equations** in [**ellipticEquations.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/ellipticEquations.mlx) <br> [<img src="Images/elliptic.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FiniteDifferenceMethods/ellipticEquations.mlx) <br> | Learn how to solve boundary value problems. <br> | \* Identify thermal sources, sinks, and reservoirs <br> \* Learn how to use iterative methods to solve solutions for steady state problems. <br> | Code Visible <br> |
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| **Solving incompressible Navier-Stokes equations** in [**flowSolver_teachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=NavierStokes/flowSolver_teachingModule.mlx) <br> [<img src="Images/streamlines_Re_1000.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=NavierStokes/flowSolver_teachingModule.mlx) <br> | Learn how to solve the 2D incompressible NSE and build the entire solver. <br> | \* Learn how to setup a staggered grid of variables <br> \* How to setup velocity and pressure boundary conditions <br> \* Learn how to solve the x and y momentum equations <br> \* Two step projection method for divergence free velocity field <br> | Code Visible <br> |
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| **Building an interface advection scheme (SLIC)** in [**interfaceAdvectionTeachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=InterfaceAdvection/interfaceAdvection_teachingModule.mlx) <br> [<img src="Images/interface.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=InterfaceAdvection/interfaceAdvection_teachingModule.mlx) <br> | Learn how to build an interface advection scheme using the Volume-of-Fluid method and the SLIC geometric reconstruction method. <br> | \* Simple line interface construction <br> \* Flux calculation <br> | Code Visible <br> |
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| **Fluid structure interaction** in [**FSI_teachingModule.mlx**](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FluidStructureInteraction/FSI_teachingModule.mlx) <br> [<img src="Images/fsi.png" width="300">](https://matlab.mathworks.com/open/github/v1?repo=MathWorks-Teaching-Resources/Computational-Fluid-Dynamics&file=FluidStructureInteraction/FSI_teachingModule.mlx) <br> | Learn how to introduce an immersed structure into the fluid domain. <br> | \* Classic immersed boundary method for elastic structures. <br> \* Direct forcing fictitious domain method for rigid bodies. <br> | Code Visible <br>
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