A unified time discontinuous Galerkin space‐time finite element scheme for non‐Newtonian power law models

Abstract

In this work, a stabilized time Discontinuous Galerkin, Space‐Time Finite Element (tDG‐ST‐FE) scheme is presented for discretizing time‐dependent viscous shear‐thinning fluid flow models, which exhibit a usual power‐law stress strain relation. The development of the proposed numerical scheme based mainly on a unified weak space‐time formulation, where simple streamline‐upwind terms have been added in the numerical scheme, for stabilizing the discretization of the associated temporal and convective terms. The original time interval is partitioned into time subintervals, resulting in a subdivision of the space‐time cylinder into space‐time subdomains. Discontinuous Galerkin techniques are applied for the time discretization between the space‐time subdomain interfaces. A stability bound is given for the derived ST‐FE scheme. In the last part numerical examples on benchmark problems are presented for testing the efficiency of the proposed method.