Liu, Xu-Dong; Tadmor, Eitan Third order nonoscillatory central scheme for hyperbolic conservation laws. (English) Zbl 0906.65093 Numer. Math. 79, No. 3, 397-425 (1998). 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) Cited in 1 ReviewCited in 62 Documents 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 Keywords:nonoscillatory recovery; finite difference schemes; conservative discretization; third-order Godunov-type scheme; hyperbolic conservation laws Citations:Zbl 0697.65068 PDFBibTeX XMLCite \textit{X.-D. Liu} and \textit{E. Tadmor}, Numer. Math. 79, No. 3, 397--425 (1998; Zbl 0906.65093) Full Text: DOI