MODIFIED LAGRANGE-GALERKIN METHODS TO INTEGRATE TIME DEPENDENT INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

摘要

A numerical study of modified Lagrange-Galerkin (MLG) methods is presented for the incompressible Navier-Stokes equations. The convergence rate of second order in time methods is numerically proved in several test examples using both the minielement (P-1 - bubble/P-1) and the P-2/P-1 Taylor-Hood element. A focus of this work is to ascertain the influence of numerical quadrature on the stability of the methods, particularly when the Reynolds number (Re) is high. All results presented in this study confirm that low order finite element MLG methods have the same accuracy as standard Lagrange-Galerkin (LG) methods, but the computational cost of solving Navier-Stokes problems is notably reduced when MLG methods are used.