Moving finite difference method for tracking a shock or steep moving front

摘要

For tracking a shock or steep moving front in the convective Partial Differential Algebraic Equations (PDAEs), some spatial discretization methods such as central, upwinding, Essentially Non-Oscillatory (ENO) and Weighted Essentially Non-Oscillatory (WENO) schemes, and the moving grid techniques are examined respectively and simultaneously with regards to accuracy, temporal performance and stability. The uniform fixed-grid method is efficient owing to relatively short CPU time. However, the solution of the Fixed Stencil (FS) approach such as the central and upwinding spatial discretization methods is unstable. Many mesh points are needed for all of the fixed grid methods to obtain enough solution accuracy. In the moving grid techniques, stability of the solution is enhanced even at small mesh numbers but it is prohibitive because of the addition of a complex and nonlinear mesh equation to solved PDAEs. The combination of the ENO/WENO schemes (based on an adaptive stencil idea) with moving grid techniques gives a stable and accurate solution even at small mesh numbers and is efficient to track a moving shock front.