A 3-D pseudo-arc-length moving-mesh method for numerical simulation of detonation wave propagation

In this paper, we propose a robust pseudo-arc-length moving-mesh method (PALM) which adopts the strategy of overall movement and block calculation for numerical simulation of detonation wave propagation in three dimensions. The pseudo-arc-length moving-mesh method involves governing equations’ evolution, mesh redistribution, and positivity-preserving analysis. Second-order finite-volume schemes and multistage total-variation-diminishing Runge–Kutta methods are used for governing equations’ evolution, while mesh redistribution is an iterative procedure that includes mesh point redistribution and cell average conservative interpolation. In addition, positivity-preserving analysis is discussed to avoid the density or pressure becoming negative in the process of numerical calculation. Finally, several numerical examples show that our method is feasible and effective. The advantage of the PALM scheme is that we can get similar results as the Monotonic Upstream-centered Scheme for Conservation Laws (MUSCL) which requires more cells and computational run time. It is demonstrated that the computational grids using the PALM scheme can capture the detonation front.