Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave

A hyperbolic conservation equation can easily generate strong discontinuous solutions such as shock waves and contact discontinuity. By introducing the arc-length parameter, the pseudo arc-length method (PALM) smoothens the discontinuous solution in the arc-length space. This in turn weakens the singularity of the equation. To avoid constructing a high-order scheme directly in the deformed physical space, the entire calculation process is conducted in a uniform orthogonal arc-length space. Furthermore, to ensure the stability of the equation, the time step is reduced by limiting the moving speed of the mesh. Given that the calculation does not involve the interpolation process of physical quantities after the mesh moves, it maintains a high computational efficiency. The numerical examples show that the algorithm can effectively reduce numerical oscillations while maintaining excellent characteristics such as high precision and high resolution.