# High-order ALE gas-kinetic scheme with unstructured WENO reconstruction

## TL;DR

This paper introduces a high-order ALE gas-kinetic scheme that combines unstructured WENO reconstruction with a two-stage temporal method, enabling accurate and robust simulations of complex flows on deforming meshes without rezoning or remapping.

## Contribution

The paper develops a novel high-order ALE gas-kinetic scheme using unstructured WENO reconstruction, eliminating the need for rezoning and remapping in moving mesh simulations.

## Key findings

- The scheme achieves high accuracy on deforming meshes.
- It preserves geometric conservation law effectively.
- Numerical tests validate robustness and accuracy.

## Abstract

In this paper, a high-order multi-dimensional gas-kinetic scheme is presented for both inviscid and viscous flows in arbitrary Lagrangian-Eulerian (ALE) formulation. Compared with the traditional ALE method, the flow variables are updated in the finite volume framework, and the rezoning and remapping steps are not required. The two-stage fourth-order method is used for the temporal discretization, and the second-order gas-kinetic solver is applied for the flux evaluation. In the two-stage method, the spatial reconstruction is performed at both initial and intermediate stage, and the computational mesh at the corresponding stage is given by the specified mesh velocity. In the moving mesh procedure, the mesh may distort severely and the mesh quality is reduced. To achieve the accuracy and improve the robustness, the newly developed WENO method \cite{un-WENO3} on quadrilateral unstructured meshes is adopted at each stage. The Gaussian quadrature is used for flux calculation. For each Gaussian point, the reconstruction performed in the local moving coordinate, where the variation of mesh velocity is taken into account. Therefore, the accuracy and geometric conservation law can be well preserved by the current scheme even with the largely deforming mesh. Numerical examples are presented to validate the performance of current scheme, where the mesh adaptation method and cell centered Lagrangian method are used to provide mesh velocity.