Development of a Dispersion Relation Equation - Preserving Pure Advection Scheme for Solving the Navier-Stokes Equations with/Without Free Surface

Abstract

In this article we develop a dispersively more accurate pure advection scheme and apply it to properly simulate incompressible free surface flow equations. According to Clebsch velocity decomposition, the incompressible flow equations are decomposed into the equations accounting respectively for the flow potential, rotation, and dissipation. For the Euler equation, the midpoint implicit symplectic time integrator is applied to approximate the temporal derivative term. For the sake of reducing numerical dispersion error, the upwinding scheme is developed to minimize the difference between the numerical and exact dispersion relation equations for the time-dependent pure advection equation in wavenumber space.

Acknowledgments

This work was supported by the National Science Council of the Republic of China under Grant 99-2221-E-002-225-MY3.