Staggered Finite Difference Schemes for Conservation Laws

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.

[1]  Lorenzo Pareschi,et al.  Implicit-explicit runge-kutta schemes and applications to hyperbolic systems with relaxation , 2010, 1009.2757.

[2]  E. Tadmor,et al.  Third order nonoscillatory central scheme for hyperbolic conservation laws , 1998 .

[3]  Alexander Kurganov,et al.  Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton-Jacobi Equations , 2001, SIAM J. Sci. Comput..

[4]  Jianxian Qiu,et al.  On the construction, comparison, and local characteristic decomposition for high-Order central WENO schemes , 2002 .

[5]  P. Lax.  Weak solutions of nonlinear hyperbolic equations and their numerical computation , 1954 .

[6]  E. Tadmor,et al.  Non-oscillatory central differencing for hyperbolic conservation laws , 1990 .

[7]  Chi-Wang Shu.  Essentially non-oscillatory and weighted essentially non-oscillatory schemes for hyperbolic conservation laws , 1998 .

[8]  E. Tadmor,et al.  New High-Resolution Central Schemes for Nonlinear Conservation Laws and Convection—Diffusion Equations , 2000 .

[9]  P. Lax,et al.  On Upstream Differencing and Godunov-Type Schemes for Hyperbolic Conservation Laws , 1983 .

[10]  Gabriella Puppo,et al.  Staggered Finite Difference Schemes for Balance Laws , 2006 .

[11]  S. Osher,et al.  High-Resolution Nonoscillatory Central Schemes with Nonstaggered Grids for Hyperbolic Conservation Laws , 1998 .

[12]  M. Carpenter,et al.  Additive Runge-Kutta Schemes for Convection-Diffusion-Reaction Equations , 2003 .

[13]  Steven J. Ruuth,et al.  Implicit-explicit Runge-Kutta methods for time-dependent partial differential equations , 1997 .

[14]  Gabriella Puppo,et al.  High-Order Central Schemes for Hyperbolic Systems of Conservation Laws , 1999, SIAM J. Sci. Comput..

[15]  Doron Levy,et al.  A Third-Order Semidiscrete Central Scheme for Conservation Laws and Convection-Diffusion Equations , 2000, SIAM J. Sci. Comput..

[16]  G. Russo,et al.  Central WENO schemes for hyperbolic systems of conservation laws , 1999 .

[17]  E. Tadmor.  Approximate solutions of nonlinear conservation laws , 1998 .

[18]  Lorenzo Pareschi,et al.  Central Runge-Kutta Schemes for Conservation Laws , 2005, SIAM J. Sci. Comput..

[19]  Centro internazionale matematico estivo. Session,et al.  Advanced Numerical Approximation of Nonlinear Hyperbolic Equations , 1998 .

[20]  S. Osher,et al.  Efficient implementation of essentially non-oscillatory shock-capturing schemes,II , 1989 .

[21]  Chi-Wang Shu,et al.  A technique of treating negative weights in WENO schemes , 2000 .