Runge-Kutta residual distribution schemesTools Warzynski, Andrzej, Hubbard, Matthew E. and Ricchiuto, Mario (2015) Runge-Kutta residual distribution schemes. Journal of Scientific Computing, 62 (3). pp. 772-802. ISSN 1573-7691 Full text not available from this repository.AbstractWe 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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