Efficient and scalable discretization of the Navier-Stokes equations with LPS modeling

Abstract

In this work, we address the solution of the Navier–Stokes equations (NSE) by a Finite Element (FE) Local Projection Stabilization (LPS) method. The focus is on a LPS 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 interpolation-stabilized structure, which only acts on the high frequency components of the flow. As a main contribution, we propose and test an efficient discretization of the model via a stable velocity-pressure segregation, using semi-implicit Backward Differentiation Formulas (BDF) in time. On the one hand, numerical studies illustrate that the solver accurately reproduces first and second-order statistics of benchmark turbulent flows for relatively coarse meshes. On the other hand, they show that the solver works in an efficient (i.e., robust and fast) way, especially when interfaced with scalable domain decomposition methods. Such scalability results are obtained on up to 16,384 cores with a near-ideal speedup.