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A compact and fast Matlab code solving the incompressible ...

A compact and fast Matlab code solving the incompressibleNavier-Stokes equations on rectangular SeiboldApplied MathematicsMassachusetts Institute of 31, 20081 IntroductionOn the following pages you find a documentation for the Matlab , as it is used forCourse : Computational Science and En-gineering IIat theMassachusetts Institute of Technology. The code can be downloaded fromtheComputational Science and Engineeringweb Itis also linked on the course web code shall be used for teaching and learning about incompressible , viscous is an example of a simple numerical method for solving the Navier-Stokes equations. Itcontains fundamental components, such as discretization on a staggered grid, an implicitviscosity step, a projection step, as well as the visualization of the solution over time. Themain priorities of the code and compactness:The whole code is one single Matlab file of about100 :The code does not use spectral methods, thus can be modified to morecomplex domains, boundary conditions, and flow :The evolution of the flow field is visualized while the simulation speed:Full vectorization and pre- solving the arising linear systemsin an initialization step results in fast time code provides: variable box sizes, grid resolution, time step, and Reynolds numbers implicit time stepping for the fluid viscosity1 visualization of pressu

formula holds for the component V, and for the Laplacian of the pressure P and the stream function Q. If the unknown quantity is stored in a large column vector, then the above approximation can be represented as a large sparse block matrix being applied from the left. Thus, solving the Poisson equations for P and Q, as well as

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