A grid-free upwind relaxation scheme for inviscid compressible flows
A new grid-free upwind relaxation scheme for simulating inviscid compressible flows is presented in this paper. The non-linear conservation equations are converted to linear convection equations with nonlinear source terms by using a relaxation system and its interpretation as a discrete Boltzmann equation. A splitting method is used to separate the convection and relaxation parts. Least squares upwinding is used for discretizing the convection equations, thus developing a grid-free scheme which can operate on any arbitrary distribution of points. The scheme is grid free in the sense that it works on any arbitrary distribution of points and it does not require any topological information like elements, faces, edges, etc. This method is tested on some standard test cases. To explore the power of the grid-free scheme, solution-based adaptation of points is done and the results are presented, which demonstrate the efficiency of the new grid-free scheme. Copyright (c) 2005 John Wiley & Sons, Ltd.
inviscid compressible flows relaxation system discrete least squares upwinding grid-free schemes diagonal form kinetic system