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Stability of 2nd ordr one sided upwind 1st order in time |
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December 8, 2014, 19:06 |
Stability of 2nd ordr one sided upwind 1st order in time
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Member
Ardalan
Join Date: Feb 2010
Location: Baku
Posts: 50
Rep Power: 16 |
As mentioned in chapter 21 of Hirsch's book:
"second-order one-sided differences in space with a first-order difference in time (explicit), is unconditionally unstable" This can be proved for linear convection equation. I want to know that whether this is true for Euler equations or not. I get converged solutions for one dimensional nozzle flow with shock by applying the above mentioned method! However some overshoots happen at shock region. Also, when I implement limiters (minmod) to my scheme, solution convergence trend stops at about L2norm(p(n+1)-p(n))=5e-5. I can't understand what is happening. |
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