An adaptive time-stepping semi-Lagrangian method for incompressible flows

Abstract

The semi-Lagrangian method is widely applied to solving the advection term of the Navier–Stokes (N–S) equations whereas the role of time step is often unclear. This article proposed an adaptive time-stepping method, which first calculates local adaptive time step based on truncation error coefficient functions, and then to obtain global time step based on an averaging function for all grid points. The new method was tested for solving 1-D and 2-D advections with different initial time steps and grid resolutions, and the transient incompressible N–S equations. Better simulation accuracy can be achieved than the cases with constant time steps.