A unified coordinates approach to computational fluid dynamics

AbstractA unified coordinate system is introduced for computational fluid dynamics, in which the grid moves with velocity hq,q being fluid velocity. It includes the Eulerian coordinates as a special case when h=0 and the Lagrangian when h=1. By suitably choosing the free function h-h=1 for 1D flow, h chosen to preserve grid angles for 2D flow, and to preserve grid skewness for 3D flow—the unified coordinate system is shown, in a large number of examples involving the Euler equations, to be superior to both Eulerian and Lagrangian ones in resolving flow discontinuities: shocks and especially slip lines. This approach is also successfully extended to shallow water waves and viscous flow