Download Essentially Non-Oscillatory and Weighted Essentially by Chi-Wang Shu PDF

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By Chi-Wang Shu

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Extra info for Essentially Non-Oscillatory and Weighted Essentially Non-Oscillatory Schemes for Hyperbolic Conservation Laws

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Characteristic-wise FD 1D system, Roe-type. 1. Compute the divided or undivided differences of the flux f (u) for all i; 2. 92). 4, for each component of the characteristic variables v, to obtain the corresponding component of the flux vˆi+ 12 . 95): fˆi+ 12 = R vˆi+ 12 3. 73). 10. Characteristic-wise FD 1D system, flux splitting. 1. Compute the divided or undivided differences of the flux f (u) and the solution u for all i; 2. 92). 5, for each component of the ± For the characteristic variables, to obtain the corresponding component of the flux gˆi+ 1.

24). 11), as here only one residue evaluation is needed per time step. Of course, the storage requirement is much bigger here. There is also the problem of the starting values u1 , u2 , u3 and u4 . 3 listed in [66]. It seems that if one uses more storage (larger m) one could get better CFL coefficients. 3. As in the Runge-Kutta case, we can relax the condition βk ≥ 0 by introducing the adjoint ˜ We thus have operator L. 4. 27) c = min k αk , |βk | ˜ for negative βk . provided that αk ≥ 0, and L is replaced by L ˜ n ) must be Again, notice that, if we have both positive and negative βk ’s, then both L(un ) and L(u computed, the cost as well as storage requirement will thus be doubled.

Characteristic-wise FD 1D system, Roe-type. 1. Compute the divided or undivided differences of the flux f (u) for all i; 2. 92). 4, for each component of the characteristic variables v, to obtain the corresponding component of the flux vˆi+ 12 . 95): fˆi+ 12 = R vˆi+ 12 3. 73). 10. Characteristic-wise FD 1D system, flux splitting. 1. Compute the divided or undivided differences of the flux f (u) and the solution u for all i; 2. 92). 5, for each component of the ± For the characteristic variables, to obtain the corresponding component of the flux gˆi+ 1.

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