Positivity-preserving moving mesh scheme for two-step reaction model in two dimensions

• We have proposed a moving mesh scheme for the two-step chemical reaction model.
• We have proposed positivity-preserving improvements for the moving mesh scheme.
• Our scheme can obtain good results with fewer grid cells.
• The front step and detonation diffraction problem is successfully simulated.
• Mesh is adaptive with the wave front in our simulations.

In this paper, we have proposed a moving mesh scheme for the two-step chemical reaction model in two dimensions. This moving mesh scheme consists of two independent parts: governing equations evolution and mesh-redistribution. The second-order finite volume scheme is used in the governing equations evolution part. In the mesh-redistribution part, the mesh points are first redistributed, and then the cell averages of the conservative variables are remapped onto the new mesh in a conservative way. In addition, the positivity-preserving improvements are shown for the two parts. The positivity-preserving thresholds guarantee the average value positive, and then an improved implementation is given to make each cell value positive. Several numerical experiments are carried out to demonstrate the accuracy and effectiveness of the proposed method.