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Primitive, conservative and adaptive schemes for hyperbolic conservation laws. (English) Zbl 0958.76062
Toro, E. F. (ed.) et al., Numerical methods for wave propagation. Selected contributions from the workshop held in Manchester, GB, May 1995. Dordrecht: Kluwer Academic Publishers. Fluid Mech. Appl. 47, 323-385 (1998).
The paper deals with construction of explicit upwind finite difference schemes for non-conservative formulations of hyperbolic conservation laws. Schemes of first, second, and third order of accuracy are constructed, and then nonlinear versions of these schemes are derived by using total variation diminishing (TVD) criteria. The general methodology is applied to four particular approaches: 1) weight average flux method; 2) MUSCL and MUSCL-Hancock data reconstruction method; 3) generalized Riemann problem method; 4) piecewise-linear method.
For the entire collection see [Zbl 0911.00052].

76M20 Finite difference methods applied to problems in fluid mechanics
76N15 Gas dynamics (general theory)
76L05 Shock waves and blast waves in fluid mechanics