Shock-capturing methods for free-surface shallow water flows
Hi everybody,
I have been reading very carefully the book by E. Toro on shock capturing methods for shallow water flows and cannot understand why it uses the criteria h*>hL (or h*>hR) to define the situation when a shock will occur. Shouldn't it be labmda*>lambdaL [where lambda is the eigenvalue of the Jacobian matrix, e.g. u+sqrt(gh)]. Does anyone has read that book and found the same issue? Thanks, Ricardo |
Lax entropy condition gives
0 > lambdaL - lambda* 0 > uL+sqrt{ghL}-(u*+sqrt{gh*}) 0 > uL-2sqrt{ghL}+3sqrt{ghL}-(u*-2sqrt{gh*}+3sqrt{gh*}) (Riemann Invariants, comes from integral curves) 0 > C - C +3(sqrt{ghL}-sqrt{gh*}) h* > hL |
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