A high-order, conservative and positivity-preserving intersection-based remapping method between meshes with isoparametric curvilinear cells

TL;DR

This paper introduces a high-order, conservative, and positivity-preserving remapping method for isoparametric curvilinear meshes that efficiently handles complex intersections and maintains physical and numerical accuracy.

Contribution

It develops a novel intersection-based remapping technique using Weiler-Atherton clipping and WENO reconstruction for high-order curved meshes, ensuring efficiency and robustness.

Findings

Achieves high-order accuracy and strict conservation.

Maintains positivity of physical quantities like density.

Handles arbitrary high-order isoparametric cells without significant computational cost.

Abstract

This paper presents a novel intersection-based remapping method for isoparametric curvilinear meshes within the indirect arbitrary Lagrangian-Eulerian (ALE) framework, addressing the challenges of transferring physical quantities between high-order curved-edge meshes. Our method leverages the Weiler-Atherton clipping algorithm to compute intersections between curved-edge quadrangles, enabling robust handling of arbitrary order isoparametric curves. By integrating multi-resolution weighted essentially non-oscillatory (WENO) reconstruction, we achieve high-order accuracy while suppressing numerical oscillations near discontinuities. A positivity-preserving limiter is further applied to ensure physical quantities such as density remain non-negative without compromising conservation or accuracy. Notably, the computational cost of handling higher-order curved meshes, such as cubic or even higher-degree parametric curves, does not significantly increase compared to secondorder curved meshes. This ensures that our method remains efficient and scalable, making it applicable to arbitrary high-order isoparametric curvilinear cells without compromising performance. Numerical experiments demonstrate that the proposed method achieves highorder accuracy, strict conservation (with errors approaching machine precision), essential non-oscillation and positivity-preserving.