Runge-Kutta Residual Distribution Schemes

Andrzej Warzynski (1) , Matthew Hubbard (1) , Mario Ricchiuto (2, 3)

1 School of Computing [Leeds]
2 BACCHUS - Parallel tools for Numerical Algorithms and Resolution of essentially Hyperbolic problems
3 IMB - Institut de Mathématiques de Bordeaux

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.

Domaines: Analyse numérique [math.NA]; Dynamique des Fluides [physics.flu-dyn]

Andrzej Warzynski, Matthew Hubbard, Mario Ricchiuto. Runge-Kutta Residual Distribution Schemes. [Research Report] RR-8370, INRIA. 2013. ⟨hal-00865154⟩