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Solution of a "simple" linear system

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Old   June 21, 2023, 12:32
Default Solution of a "simple" linear system
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Matthew
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Suppose I have the linear system:

rho_t+Urho_x+rho_0v_x=0

v_t+Uv_x=Dv_xx+aT_x

T_t+UT_x=kT_xx+bv_x

This is a mixed system of equations, one hyperbolic and two parabolic. I thought about upwinding the first-order derivatives and doing central difference for the second-order derivatives. The domain is for 0<=x<=1, and t>0.

The method I used failed completely, I was using explicit Euler, with a low CFL number to get convergence, but the results were haywire.

Any suggestions on how to get started?
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