A Conservative Shock Fitting Method on Unstructured Grids

A dynamic discontinuity tracking method to achieve shock fitting is presented. The method is based on the properties of Roe's scheme which becomes an exact Riemann solver when grid lines are aligned with the discontinuity. To make full use of this property, a technique that moves and adapts the grid in order to align and position element interfaces on the discontinuities is proposed. This algorithm is implemented with a conventional two-dimensional finite volume solver on unstructured triangular meshes. The method's ability to retrieve the exact solution is investigated on simple problems having analytical solutions.