An ALE pairwise-relaxing meshless method for compressible flows

In this paper, we present a pairwise-relaxing meshless (PRM) method for solving the Euler equations of compressible flows within the Arbitrary Lagrangian Eulerian (ALE) framework. Derived from the moving particle semi-implicit (MPS) method and the finite volume particle (FVP) method, the PRM approximates the derivatives from the value defined at the midpoint of each interacting particle pairs through a kernel-based formulation. Pairwise-relaxing constants are introduced to the kernels to provide degree of freedom to enforce the Taylor-series consistency condition while mass, momentum and energy are conserved exactly. An upwind high-order reconstruction scheme via a corrective procedure and variable cut-off radius is also developed for this PRM method. The HLLC approximate Riemann solver is adopted to solve Riemann problem. One and two-dimensional numerical tests are presented to demonstrate the performance of the PRM method.