High order semi-Lagrangian methods for the incompressible Navier-Stokes equations
This work provides a new numerical method for computational fluid dynamics, offering improved accuracy for convection-dominated flows, though it is an incremental extension of existing semi-Lagrangian and spectral element techniques.
The authors developed high-order semi-Lagrangian methods for incompressible Navier-Stokes equations, achieving up to third-order accuracy in space and time, with demonstrated good performance on convection-dominated problems.
We propose a class of semi-Lagrangian methods of high approximation order in space and time, based on spectral element space discretizations and exponential integrators of Runge-Kutta type. We discuss the extension of these methods to the Navier-Stokes equations, and their implementation using projections. Semi-Lagrangian methods up to order three are implemented and tested on various examples. The good performance of the methods for convection-dominated problems is demonstrated with numerical experiments.