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Third order nonoscillatory central scheme for hyperbolic conservation laws. (English) Zbl 0906.65093
A third-order Godunov-type scheme for hyperbolic conservation laws is constructed along the lines of a second-order scheme on staggered grids as developed by H. Nessyahu and E. Tadmor [J. Comput. Phys. 87, No. 2, 408-463 (1990; Zbl 0697.65068)] some years earlier. Again a staggered grid is used and piecewise parabolic recovery of point values from cell averages is employed such that the resulting scheme is nonoscillatory. Since the constructed scheme results in a central discretization several advantages over upwind approximations are gained in the case of systems of conservation laws. In particular, no approximate Riemann solver is necessary and nor a field-by-field characteristic decomposition.
Reviewer: Th.Sonar (Hamburg)

MSC:
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
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