Staggered Finite Difference Schemes for Conservation Laws

被引：0
作者：
Gabriella Puppo
Giovanni Russo
机构：
[1] Politecnico di Torino,Dipartimento di Matematica
[2] Università di Catania,Dipartimento di Matematica ed Informatica
来源：
Journal of Scientific Computing | 2006年 / 27卷
关键词：
Conservation laws; balance laws; finite difference schemes; high-order accuracy; central schemes;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this work, we introduce new finite-difference shock-capturing central schemes on staggered grids. Staggered schemes may have better resolution of the corresponding unstaggered schemes of the same order. They are based on high-order nonoscillatory reconstruction (ENO or WENO), and a suitable ODE solver for the computation of the integral of the flux. Although they suffer from a more severe stability restriction, they do not require a numerical flux function. A comparison of the new schemes with high-order finite volume (on staggered and unstaggered grids) and high order unstaggered finite difference methods is reported.
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页码：403 / 418
页数：15
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  • [1] Asher U.(1997)Implicit-explicit Runge–Kutta methods for time dependent partial differential equations Appl. Numer. Math. 25 151-167
  • [2] Ruuth S.(1999)High order central schemes for hyperbolic systems of conservation laws SIAM J. Sci. Comput. 21 294-322
  • [3] Spiteri R.J.(1983)On upstream differencing and Godunov-type schemes for hyperbolic conservation laws SIAM Rev. 25 35-61
  • [4] Bianco F.(1998)High-resolution nonoscillatory central schemes with nonstaggered grids for hyperbolic conservation laws SIAM J. Numer. Anal. 35 2147-2168
  • [5] Puppo G.(2003)Additive Runge-Kutta schemes for convection-diffusion-reaction equations Appl. Numer. Math. 44 139-181
  • [6] Russo G.(2001)Semi-discrete central-upwind scheme for hyperbolic conservation laws and Hamilton Jacobi equations SIAM J. Sci. Comput. 23 707-740
  • [7] Harten A.(2000)New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations J. Comput. Phys. 160 241-282
  • [8] Lax P.D.(2000)A third-order semidiscrete central scheme for conservation laws and convection-diffusion equations SIAM J. Sci. Comput. 22 1461-1488
  • [9] van Leer B.(1954)Weak solutions of non-linear hyperbolic equations and their numerical computation CPAM. 7 159-193
  • [10] Jiang G.-S.(1999)Central WENO schemes for hyperbolic systems of conservation laws Math. Model Numer. Anal. 33 547-571
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