Towards High-order Accurate Numerical Simulation of Unsteady Flow Physics over Domains with Large Deformation

Abstract

This paper presents the development of a high-order flux reconstruction (FR) formulation for unsteady flow simulation with dynamic grid algorithms. Specifically, the high-order FR formulation for the Navier-Stokes equations in an arbitrary Lagrangian-Eulerian (ALE) format is developed for numerical simulation on moving domains. A hybrid moving grid algorithm consisting of algebraic grid smoothing and grid regeneration methods is developed to resolve domains with large deformation. The ‘dist-mesh’ technique is used for mesh regeneration, and local Lagrange interpolation within finite elements is used for flow field reconstruction. Several unsteady flow cases are studied to verify the effectiveness of the new method developed in this work.