Symplectic Semi-Lagrangian Schemes for Computational Fluid Dynamics

Abstract

The symplectic semi-Lagrangian (SSL) method was developed in order to improve the preservation of the physical quantities of the semi-Lagrangian method. In this method, symplectic integrators are adopted in searching for the upstream point in the semi-Lagrangian method. The purpose of this paper is to verify the validity of the SSL method for a simple passive scalar advection (PSA) problem and for a more practical fluid problem, two-dimensional incompressible viscous flow. From the computed results, it is confirmed that the SSL can take a large time-step size over Courant number 2 without losing computational accuracy.

Keywords:

• Symplectic integrator
• CFD
• Passive scalar advection
• Incompressible fluid flow
• Karman vortex shedding

Additional information

Notes on contributors

Nobuatsu Tanaka