An ALE residual distribution scheme for the unsteady Euler equations over triangular grids with local mesh adaptation

TL;DR

This paper introduces a novel residual distribution scheme for unsteady Euler equations on triangular grids with local mesh adaptation, avoiding interpolation and ensuring conservation and stability.

Contribution

It presents an interpolation-free mesh adaptation technique within the ALE framework that preserves numerical properties and enforces the geometric conservation law.

Findings

Successfully applied to 2D steady and unsteady flow simulations

Achieves high-order accuracy on unstructured grids

Prevents spurious oscillations in dynamic domains

Abstract

This work presents a novel interpolation-free mesh adaptation technique for the Euler equations within the arbitrary Lagrangian Eulerian framework. For the spatial discretization, we consider a residual distribution scheme, which provides a pretty simple way to achieve high order accuracy on unstructured grids. Thanks to a special interpretation of the mesh connectivity changes as a series of fictitious continuous deformations, we can enforce by construction the so-called geometric conservation law, which helps to avoid spurious oscillations while solving the governing equations over dynamic domains. This strategy preserves the numerical properties of the underlying, fixed-connectivity scheme, such as conservativeness and stability, as it avoids an explicit interpolation of the solution between different grids. The proposed approach is validated through the two-dimensional simulations of steady and unsteady flow problems over unstructured grids.