Imex Finite Volume Evolution Galerkin Scheme for Three-dimensional Weakly Compressible Flows.∗

In this paper we will derive an implicit-explicit (IMEX) finite volume evolution Galerkin scheme for three-dimensional Euler equations. We will in particular concentrate a singular limit of weakly compressible flows when the Mach number is about O(10−2)−O(10−6). In order to efficiently resolve slow dynamics we split the whole nonlinear system in a stiff linear part governing the acoustic and gravitational waves and a non-stiff nonlinear part that models nonlinear advection effects. We use stiffly accurate second order IMEX scheme for time discretization to approximate stiff linear operator implicitly and the non-stiff nonlinear operator explicitly. Furthermore in order to take multdimensional effects of flow propagation into account we apply three-dimensional evolution Galerkin operator.