Following the directions of the module called "12 steps to Navier-Stokes equations" at Boston University: https://lorenabarba.com/blog/cfd-python-12-steps-to-navier-stokes/
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1-D Linear Convection
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1-D Diffusion
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2-D Linear Convection
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2-D Non Linear Convection
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2-D Diffusion
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2-D Non Linear Convection with Diffusion