An efficient time-splitting approximation of the Navier–Stokes equations with LPS modeling

Abstract

In this work, the solution of the Navier–Stokes equations (NSE) is addressed by a Finite Element (FE) Local Projection Stabilization (LPS) method combined with an efficient time-splitting approximation strategy. The focus is on the high-order term-by-term stabilization method that has one level, in the sense that it is defined on a single mesh, and in which the projection-stabilized structure of standard LPS methods is replaced by an alternative interpolation-stabilized structure. The main contribution is on numerically analyzing for the cited LPS method the proposed time approximation via stable velocity–pressure segregation, using semi-implicit Backward Differentiation Formulas (BDF). An overview about theoretical results from the numerical analysis of the proposed method is given, by highlighting the used mathematical tools. Numerical studies support the analytical results and illustrate the potential of the method for the efficient and accurate simulation of turbulent flows on relatively coarse grids. Smooth unsteady flows are simulated with optimal order of accuracy.