An adaptive discontinuity fitting technique on unstructured dynamic grids

A novel, adaptive discontinuity fitting technique has been further developed on unstructured dynamic grids to fit both shock waves and contact discontinuities in steady flows. Moreover, in order to efficiently obtain shock-fitting solutions, two strategies, direct-fitting and indirect-fitting, have been proposed to, respectively, deal with simple and complex flows. More specifically, without first computing the flow field by a shock-capturing method, the direct-fitting strategy, mainly dealing with these discontinuities of which topologies are clearly known, can quickly obtain the solutions by initially presetting an approximate discontinuity front. By contrast, the indirect-fitting strategy, especially in coping with the complicated discontinuity structures, must utilize both shock-capturing solutions and shock detection techniques to first determine initial discontinuity locations. The two strategies have been successfully applied to a series of compressible flows, including a two-dimensional flow with type IV shock–shock interaction and a three-dimensional flow with type VI interaction. In addition, comparing the fully-fitting solution with the partially-fitting solution in the discontinuity interaction region, it is indicated that an accurate result can be acquired if all the discontinuities in the vicinity of interaction points are fully fitted. Nevertheless, the computational accuracy of expansion waves can indeed significantly affect the downstream discontinuities.