Relaxation Deferred Correction Methods and their Applications to Residual Distribution Schemes

A class of residual distribution schemes and their relation to relaxation systems

Residual distributions (RD) schemes are a class of of high-resolution finite volume methods for unstructured grids. A key feature of these schemes is that they make use of genuinely multidimensional (approximate) Riemann solvers as opposed to the piecemeal 1D Riemann solvers usually employed by finite volume methods. In 1D, LeVeque and Pelanti [J. Comp. Phys. 172, 572 (2001)] showed that many o...

Sequential Methods and Their Applications

Runge-Kutta residual distribution schemes

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 ...

Upwind and High-Resolution Methods for Compressible Flow: From Donor Cell to Residual- Distribution Schemes

In this paper I review three key topics in CFD that have kept researchers busy for half a century. First, the concept of upwind differencing, evident for 1-D linear advection. Second, its implementation for nonlinear systems in the form of highresolution schemes, now regarded as classical. Third, its genuinely multidimensional implementation in the form of residual-distribution schemes, the mos...

Residual Distribution Schemes on Quadrilateral Meshes

We propose an investigation of the residual distribution schemes for the numerical approximation of two dimensional hyperbolic systems of conservation laws on general quadrilateral meshes. In comparison to the use of triangular cells, usual basic features are recovered, an extension of the Upwinding concept is given, and a Lax-Wendroff like theorem is adapted for consistency. We show how to ret...