A front tracking method on unstructured grids

Abstract A numerical method is developed for tracking discontinuities which is integrated in a generalized finite-volume solution framework for systems of conservation laws on unstructured grids of arbitrary element type. The location, geometry and the movement of the discontinuities are described by a local level set method on a restricted, dynamic definition range. Special algorithms based on least square methods are developed for handling the transport and renormalization of the level set function within the restricted range. An additional error correction is employed to minimize topological errors of the tracked front geometry. The jump conditions at the front are updated by one-sided extrapolation which define the local front velocity and the Riemann problem. A flux separation concept enables the treatment of the discontinuity within the finite-volume concept. The front tracking method is demonstrated by a number of computational examples for shock wave problems.

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