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Solution of a "simple" linear system

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June 21, 2023, 13:32	Solution of a "simple" linear system	#1
hunt_mat Senior Member Matthew Join Date: Mar 2022 Location: United Kingdom Posts: 184 Rep Power: 4	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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