Extension of piecewise exact solution method for two- and three-dimensional fluid flows

Abstract

Extended forms of a pseudo-numerical scheme for advection terms in fluid momentum equations are proposed here. The fact that analytic solution exists for the Burgers equation, if velocity distribution in space is straight for one-dimensional flow, was shown by Jang et al. Analytic solution also exists for two- or three-dimensional fluid flows, if the velocity components in two-or three-direction are linearly distributed in space, and the existing piecewise exact solution method is extended for two- and three-dimensions here. The analytic solution is adopted for computation of the advecting property of fluid momentum in two- or three-dimensional directions. This method produces zero numerical error during one time increment so that it is distinguished from any other numerical scheme which produces small or large numerical error within one time increment. The behavior of the new scheme is demonstrated for two-and three-dimensional examples. The nonlinear modifications of velocity profiles towards singularity with time progress are well simulated for three test cases. The computed maximum relative errors for a given condition for one-, two-, and three-dimensions become larger as the number of dimension increases. The scheme is believed to work well for two-and three-dimensional flows.