Abstract:
One way to achieve high degree fidelity in the whole flow field is by developing shock-fitting methods combined with high-order finite difference schemes. After all the discontinuities in shock-embedded compressible fluid flow are assembled, the application of the high-order finite difference schemes becomes the main problem which we need to consider. It has been found that the finite difference schemes always make numerical errors under curvilinear coordinate system due to the unfulfilled geometric conservation law. Moreover, we found that the errors of high-order schemes are greater than that of first-order upwind scheme for uniform flow. The reason given in this paper is that the stencils of high-order schemes involve more mesh points than that of first-order scheme. The source-coupled algorithm based on discrete equivalence equations proposed by the authors can eliminate the errors. Besides, the problem of normal shock's motion on uniform grid is also discussed in this paper. Because of the flux splitting, two waves can be created after the moving normal shock. These two waves travel at two different characteristic velocities, and can lead to numerical turbulence when the shock does not exactly match to grid points. Since the shock-capture methods assume that shock is spatial continuous, transition regions represented by the numerical solution leads to difficulties in the credibility evaluation. Shock-fitting methods can avoid this problem.