Analytic solution for 2D steady Euler equations
I'm trying to verifiy my CFD code for low Mach number flows with some analytical or manufactured solutions.
The convection and/or diffusion equation for a scalar is fine and now I focus on the Navier Stokes equations:
First, I want to check the non linear convection term, so I suppress the viscosity considering a perfect fluid and starting from the Green Taylor vorticies solution for Navier Stokes:
I get this solution:
which satisfies the steady Euler equations:
I tried this solution with my CFD code setting boundary and initial conditions with the solution, the pressure is also imposed, not computed, with the solution.
At each iteration, I solve the velocity components and then update the convective flux, solve velocity, update the convective flux, etc. I use finite volume, upwind or centered convective scheme.
My problem: after some oscillations, the flow diverges and I don't understand why. Is the solution unstable ? Can't a solver for Navier Stokes solve an Euler problem ?
Did or is anybody try this kind of problem ?
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