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

An algorithm based on the finite element modified method of characteristics (FEMMC) is presented to solve convection-diffusion, Burgers and unsteady i ncompressible 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 ou r method. To solve the Navier-Stokes equations, an approach that can be con ceived as a fractional step method is used. The innovative first stage of o ur method is a backward search and interpolation at the foot of the charact eristics, which we identify as the convective step. In this particular work , this step is followed by a conjugate gradient solution of the remaining S tokes problem. Numerical results are presented for: (a) Convection-diffusion equation. Gaussian hill in a uniform rotating fiel d. (b) Burgers equations with viscosity. (c) Navier-Stokes solution of lid-driven cavity flow at relatively high Rey nolds numbers. (d) Navier-Stokes solution of flow around a circular cylinder at Re = 100. Copyright (C) 2000 John Wiley & Sons, Ltd.