Runge-Kutta Residual Distribution Schemes
RICCHIUTO, Mario
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
RICCHIUTO, Mario
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
< Réduire
Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems [BACCHUS]
Institut de Mathématiques de Bordeaux [IMB]
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en
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Ce document a été publié dans
2013-09-24
Résumé en anglais
We are concerned with the solution of time-dependent nonlinear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in ...Lire la suite >
We are concerned with the solution of time-dependent nonlinear hyperbolic partial differential equations. We investigate the combination of residual distribution methods with a consistent mass matrix (discretisation in space) and a Runge-Kutta-type time stepping (discretisation in time). The introduced nonlinear blending procedure allows us to retain the explicit character of the time stepping procedure. The resulting methods are second order accurate provided that both spatial and temporal approximations are. The proposed approach results in a global linear system that has to be solved at each time-step. An efficient way of solving this system is also proposed. To test and validate this new framework, we perform extensive numerical experiments on a wide variety of classical problems.< Réduire
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