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On the resolution and stability of central difference schemes. (English) Zbl 1063.65092
Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 793-800 (2002).
Summary: We present several improvements for the Jiang-Nessyahu-Tadmor second-order, nonoscillatory, central difference scheme on two-dimensional, staggered, Cartesian grids for systems of conservation laws [cf. G. S. Jiang and E. Tadmor, SIAM J. Sci. Comput. 19, No. 6, 1892–1917 (1998; Zbl 0914.65095); H. Nessyahuh and E. Tadmor, J. Comput. Phys. 87, No. 2, 408–463 (1990; Zbl 0697.65068)]. They concern the flux quadrature to reduce grid orientation effects, a more powerful version of A. Harten’s artificial compression method [ibid. 49, 357–393 (1983; Zbl 0565.65050)] to improve the resolution of linear discontinuities, some experiments and analysis of instabilities in 2D as well as an adaptive staggered scheme on structured Cartesian grids.
65M12Stability and convergence of numerical methods (IVP of PDE)
65M06Finite difference methods (IVP of PDE)
35L65Conservation laws
65M50Mesh generation and refinement (IVP of PDE)