The High-order Accuracy of a Numerical Analysis for the Advective Equation by Finite Difference Methods

Abstract

The representative finite difference methods and explicit time-marching methods, which have been ploposed for high-Reynolds-numbers flow and for vectorization, are compared by solving the rotating cone problem of the advective equation. The convective term is approximated by the second order central, QUICK, the third-order upwind and the fourth-order central difference methods. The high-order time-marching methods are used, e.g. the second-order or the third-order Adams-Bashforth method, the Predictor-Corrector method and the four-stage Runge-Kutta method. The QUICKEST method and LEITH method for the high-order accuracy calculation to the discretization of space and time marching, respectively, are also discussed.