Finite element modified method of characteristics for the Navier-Stokes equations

Abstract

An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection-diffusion, Burgers and unsteady incompressible Navier-Stokes equations for laminar flow. Solutions for these progressively more involved problems are presented so as to give numerical evidence for the robustness, good error characteristics and accuracy of our method. To solve the Navier-Stokes equations, an approach that can be conceived as a fractional step method is used. The innovative first stage of our method is a backward search and interpolation at the foot of the characteristics, which we identify as the convective step. In this particular work, this step is followed by a conjugate gradient solution of the remaining Stokes problem. Numerical results are presented for: (a) Convection-diffusion equation. Gaussian hill in a uniform rotating field. (b) Burgers equations with viscosity. (c) Navier-Stokes solution of lid-driven cavity flow at relatively high Reynolds numbers. (d) Navier-Stokes solution of flow around a circular cylinder at Re = 100.