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Zbl 1063.65092
Lie, Knut-Andreas; Noelle, Sebastian; Rosenbaum, Wolfram
On the resolution and stability of central difference schemes. (English)
[A] 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. 793-800 (2002). ISBN 1-9039-9634-1/pbk

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. {\it G. S. Jiang} and {\it E. Tadmor}, SIAM J. Sci. Comput. 19, No. 6, 1892--1917 (1998; Zbl 0914.65095); {\it H. Nessyahuh} and {\it 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 {\it 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.

MSC 2000:: *65M12 Stability and convergence of numerical methods (IVP of PDE)
65M06 Finite difference methods (IVP of PDE)
35L65 Conservation laws
65M50 Mesh generation and refinement (IVP of PDE)

Keywords: numerical examples; stability; flux quadrature; artificial compression; adaptive staggered grids; central difference scheme; systems of conservation laws

Citations: Zbl 0914.65095; Zbl 0697.65068; Zbl 0565.65050

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