A Highly Accurate Modified Method of Characteristics for Convection–dominated Flow Problems

Abstract

AbstractHigh-order accurate methods for convection-dominated flow problems have the potential to reduce the computational effort required for a given order of solution accuracy. The state of the art in this field is more advanced for Eulerian methods than for semi-Lagrangian methods. In this paper, we introduce a new higher order approach that is based on combining the modified method of characteristics with the gradients computed during solution reconstruction. Special attention is given to the class of third-order schemes which uses a higher-order method to calculate the departure points and a high-order polynomial reconstruction to interpolate the solution at the characteristic feet. Numerical experiments are carried out on several benchmark transport-diffusion equations including incompressible Navier-Stokes problems. The computed results support our expectations for a robust and high-order accurate method.