A high-order rectilinear Lagrangian method based on the geometric conservation law

TL;DR

This paper introduces a high-order Lagrangian mesh moving strategy for quadrilateral meshes that ensures geometric conservation and high accuracy, validated by vortex test cases.

Contribution

It proposes a novel mesh moving method based on area conservation and velocity asymptotics, enhancing geometric fidelity and accuracy in high-order Lagrangian schemes.

Findings

The scheme adheres strictly to geometric conservation laws.

It achieves high-order accuracy verified by vortex tests.

The method is feasible for smooth flow simulations.

Abstract

This paper presents a mesh moving strategy for high-order Lagrangian method on quadrilateral meshes. The primary evidence of this method stems from principle of area conservative linearization and the asymptotic properties of the velocity. The former strictly adheres to the requirements of geometric conservation laws, while the latter provides a high-order accuracy guarantee. Two smooth vortex test cases verify the feasibility of the proposed scheme.