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 jojo81 October 15, 2012 12:05

Analytic solution for 2D steady Euler equations

Hello,

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 ?

Thanks.

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