Runge–Kutta Residual Distribution Schemes |
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Authors: | Andrzej Warzyński Matthew E Hubbard Mario Ricchiuto |
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Affiliation: | 1.School of Computing,University of Leeds,Leeds,UK;2.INRIA Bordeaux Sud-Ouest,Talence Cedex,France |
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Abstract: | We are concerned with the solution of time-dependent non-linear 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 non-linear 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. An extensive numerical comparison of our approach with other multi-stage residual distribution schemes is also given. |
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