Variational Multiscale Stabilization Method for Compressible Flows

Abstract

This paper describes a Variational Multiscale method for Compressible flows, VMSC, firstly presented in [1,2,6]. While the VMS method was introduced by Hughes and coworkers [3] in the context of incompressible flows, it is not until very recently that compressible flow has being addressed to be stabilized following these ideas. A version for mixed Finite Volumes method is proposed in [4] and a first version for supersonic flow is presented in [5]. In the present paper, we derive a totally new formulation for a wide range of Mach numbers, analyzing different linearization strategies and stabilization parameter tau, modeled as a “ non - diagonal” s tabiliza tion para meter matrix. The wide range of M ach numbers is tested with examples ranging from transient atmospheric flows benchmarks up to hypersonic flows. For the case of supersonic flows, an anisotropic shock-capturing diffusion is added. Viscous problems are addressed, particularly supersonic ones with temperature dependent viscosities. In this paper, the explicit version of the VMC-C algorithm is addressed, parallelized with almost linear scalability up to thousands of processors, extending the tests of [1,2,6] and focusing mainly in implementation issues.