An ale formulation for compressible flows based on multi-moment finite volume method

Abstract

A direct Arbitrary Lagrangian Eulerian (ALE) formulation using multi-moment finite volume method for viscous compressible flows on unstructured moving grids has been developed and presented in this paper. High-order polynomials are reconstructed over a compact mesh stencil by making use of both volume integrated average value (VIA) and point values (PV) at the vertices of mesh cells which change in time. By formulating the governing equation in ALE integral form and differential form, the computational variables, VIA and PV, are updated, respectively, by a finite volume scheme and a point-wise discretization using multi-moments (VIA and PV). A simple and efficient formulation is derived for moving mesh which satisfies the geometrical conservation law. In the computations involving moving-body, the PVs of velocity at the vertices of cells adjacent to the body surface are coincided with the motion of the body, which eliminates the numerical approximation to find the cell boundary values on the body surface in conventional finite volume method. Numerical tests are presented to verify the present method as a high-order ALE formulation for compressible flows on both stationary and moving grids.