Locally Conservative, Stabilized Finite Element Methods for a Class of Variable Coefficient Navier-Stokes Equations

摘要

Computer simulation of three-dimensional incompressible flow is of interest in many navigation, coastal, and geophysical applications. This report is the fifth in a series of publications that documents research and development on a state-of-the-art computational modeling capability for fully three-dimensional two-phase fluid flows with vessel/ structure interaction in complex geometries. It is primarily concerned with model verification, often defined as 'solving the equations right'. Model verification is a critical step on the way to producing reliable numerical models, but it is a step that is often neglected. Quantitative and qualitative methods for verification also provide metrics for evaluating numerical methods and identifying promising lines of future research. Fully-three dimensional flows are often described by the incompressible Navier-Stokes (NS) equations or related model equations such as the Reynolds Averaged Navier Stokes (RANS) equations and Two-Phase Reynolds Averaged Navier-Stokes equations (TPRANS).We will describe spatial and temporal discretization methods for this class of equations and test problems for evaluating the methods and implementations. The discretization methods are based on stabilized continuous Galerkin methods (variational multiscale methods) and discontinous Galerkin methods. The test problems are taken from classical fluid mechanics and well-known benchmarks for incompressible flow codes. We demonstrate that the methods described herein meet three minimal requirements for use in a wide variety of applications: 1) they apply to complex geometries and a range of mesh types; 2) they robustly provide accurate results over a wide range of flow conditions; and 3) they yield qualitatively correct solutions, in particular mass and volume conserving velocity approximations.