A Direct ALE Multi-Moment Finite Volume Scheme for the Compressible Euler Equations (Communications in Computational Physics, 2018)
A direct Arbitrary Lagrangian Eulerian (ALE) method based on multi-momentfinite volume scheme is developed for the Euler equations of compressible gasin 1D and 2D space. Both the volume integrated average (VIA) and the point values(PV) at cell vertices, which are used for high-order reconstructions, are treated as thecomputational variables and updated simultaneously by numerical formulations in integraland differential forms respectively. The VIAs of the conservative variables aresolved by a finite volume method in the integral form of the governing equations toensure the numerical conservativeness; whereas, the governing equations of differentialform are solved for the PVs of the primitive variables to avoid the additional sourceterms generated from moving mesh, which largely simplifies the solution procedure.Numerical tests in both 1D and 2D are presented to demonstrate the performance ofthe proposed ALE scheme. The present multi-moment finite volume formulation consistentwith moving meshes provides a high-order and efficient ALE computationalmodel for compressible flows.
Keywords: Compressible Euler equations; multi-moment finite volume method; direct ALE; Roe Riemann solver; HLLC Riemann solver; shock waves.