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person123

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- TL;DR Summary
- Modelling a 2 dimensional, incompressible, non-viscous fluid under steady flow using Euler's equations and the finite difference method seems to lead to over-constrained boundary conditions.

Hi! I want to use Euler's equations to model a 2 dimensional, incompressible, non-viscous fluid under steady flow (essentially the simplest case I can think of). I'm trying to use the finite difference method and convert the differential equations into matrices to be solved using MATLAB. I set each pressure and velocity term into a vector (with three vectors representing u, v, and p) and the differential operators representing matrices. It seems the RHS needs all the boundary conditions for pressure, velocity in x, and velocity in y which I think over constrains the problem and could lead to impossible situations (e.g. the velocity points inward in all directions). Does anyone know how to correct this? Thanks!