TVB uniformly high-order schemes for conservation laws

Shu, Chi-Wang

doi:10.1090/S0025-5718-1987-0890256-5

TVB uniformly high-order schemes for conservation laws
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Math. Comp. 49 (1987), 105-121 Request permission

Abstract:

In the computation of conservation laws ${u_t} + f{(u)_x} = 0$, TVD (total-variation-diminishing) schemes have been very successful. But there is a severe disadvantage of all TVD schemes: They must degenerate locally to first-order accuracy at nonsonic critical points. In this paper we describe a procedure to obtain TVB (total-variation-bounded) schemes which are of uniformly high-order accuracy in space including at critical points. Together with a TVD high-order time discretization (discussed in a separate paper), we may have globally high-order in space and time TVB schemes. Numerical examples are provided to illustrate these schemes.

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