A pseudo arc-length method for strong discontinuity of detonation wave and its man manufactured solution verification

In this paper we studied a pseudo arc-length method for high-precision and high-resolution calculation, a problem that has been a great challenge for numerical simulation of strong discontinuity for explosion shock wave. By the introduction of the arc-length parameters, the mesh will move adaptively and gather automatically in the strong discontinuity singular areas, which will help to improve the grid resolution. We wrote 2D programs based on theoretical work, and conducted the program verification using the man maufactured solution. Through error analysis and numerical results, it was demonstrated that this method was more efficient in improving the calculation accuracy than the finite volume method. Finally we applied the pseudo arc-length method to 2D gas detonation wave propagation problems and studied the capture effect in the wave front and the formation of detonation cellular structure.