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 cal- culation 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 phys- ical 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.

State Key Laboratory of Explosion Science and Technology,Beijing Institute of Technology,Beijing 100081,China

[1]Tianbao MA;Chentao WANG;Xiangzhao XU-.Conservative high precision pseudo arc-length method for strong discontinuity of detonation wave)[J].应用数学和力学（英文版）,2022(03):417-436

smoothens

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