A new second-order bound-preserving conservative remapping algorithm in the ALE method

When the Euler equations are solved using Lagrangian scheme, the fact that computational cells exactly follow fluid particles may result in severe grid deformation, even more cause inaccuracy and even breakdown of the computation in some cases. So it needs to rezone meshes and remap physical quantities when the deformation of computational grid is severe. Based on the second-order Lagrangian schemes that using the discontinuous Galerkin method to solve the Euler equations, a conservative remapping scheme is proposed. This remapping scheme has two steps:the first step is using the existing remapping method to obtain the approximate average values in the new cells, then using the repair algorithm to ensure the average values in the range of local bounds; the second step is using the average values to reconstruct the linear polynomial in the new cell, and using Van Leer limiter to limit the gradient of this linear polynomial to ensure no new extremum. Results of some numerical tests are presented and demonstrate that this remapping scheme is second-order accurate, conservative and bound-preserving.