Reconstructed discontinuous Galerkin method for compressible flows in arbitrary Lagrangian-Eulerian formulation

TL;DR

This paper introduces a high-order reconstructed discontinuous Galerkin method in ALE formulation for simulating 2D compressible flows on moving, deforming domains with unstructured curved meshes, ensuring accuracy and boundary handling.

Contribution

It develops a novel high-order rDG-ALE method with GCL satisfaction and RBF-based mesh motion propagation for complex moving boundary problems.

Findings

Achieves high-order spatial and temporal accuracy.

Successfully handles complex moving boundary problems.

Maintains mesh quality with RBF interpolation.

Abstract

We present a high-order accurate reconstructed discontinuous Galerkin (rDG) method in arbitrary Lagrangian-Eulerian (ALE) formulation, for solving two-dimensional compressible flows on moving and deforming domains with unstructured curved meshes. The Taylor basis functions in use are defined on the time-dependent domain, on which also the integration and computations are performed. A third order ESDIRK3 scheme is employed for the temporal integration. The Geometric Conservation Law (GCL) is satisfied by modifying the grid velocity terms on the right-hand side of the discretized equations at Gauss quadrature points. To avoid excessive distortion and invalid elements near the moving boundary, we use the radial basis function (RBF) interpolation method for propagating the mesh motion of the boundary nodes to the interior of the mesh. Several numerical examples are performed to verify the designed spatial and temporal orders of accuracy, and to demonstrate the ability of handling moving boundary problems of the rDG-ALE method.