High-order compact ALE gas-kinetic scheme on three-dimensional unstructured meshes
Abstract
In this paper, a compact high-order gas-kinetic scheme (HGKS) is developed for compressible arbitrary Lagrangian-Eulerian (ALE) computations on three-dimensional unstructured meshes. To achieve high-order spatial accuracy, a large number of matrix inversions are required for spatial reconstruction. In ALE computations, the mesh moves and the geometric information must be recalculated at each time step, which reduces computational efficiency. To improve efficiency, a memory-reduction reconstruction strategy is employed to construct a quadratic polynomial on unstructured meshes. By differentiating the candidate polynomial, the quadratic terms are obtained by the least-squares method using the average gradient values of the cell itself and its neighboring cells. The linear terms of the polynomial are also determined by the least-squares method. On three-dimensional unstructured meshes, a 3×3 coefficient matrix must be stored, and four least-squares procedures are required to construct a quadratic polynomial. To suppress numerical oscillations in flows with discontinuities, generalized essentially non-oscillatory (GENO) reconstruction and a gradient compression factor are adopted. To accelerate the computation, a multi-GPU accelerated code is implemented using Compute Unified Device Architecture (CUDA) and Message Passing Interface (MPI). The current scheme is fully explicit, and the acceleration framework can be developed based on cell-level parallelism. Numerical examples are presented to evaluate the accuracy and robustness of the scheme, including flows with strong discontinuities, pitching wings, and helicopter rotors. Numerical results confirm the excellent performance of the compact ALE scheme on unstructured meshes.
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BibTeX
@misc{wang2026highorder,
title = {{High-order compact ALE gas-kinetic scheme on three-dimensional unstructured meshes}},
author = {Yibo Wang and Xing Ji and Liang Pan},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.05095},
eprint = {2611.05095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.05095},
}
RIS
TY - UNPB
TI - High-order compact ALE gas-kinetic scheme on three-dimensional unstructured meshes
AU - Yibo Wang
AU - Xing Ji
AU - Liang Pan
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.05095
UR - https://arxiv.org/abs/2611.05095
AB - In this paper, a compact high-order gas-kinetic scheme (HGKS) is developed for compressible arbitrary Lagrangian-Eulerian (ALE) computations on three-dimensional unstructured meshes. To achieve high-order spatial accuracy, a large number of matrix inversions are required for spatial reconstruction. In ALE computations, the mesh moves and the geometric information must be recalculated at each time step, which reduces computational efficiency. To improve efficiency, a memory-reduction reconstruction strategy is employed to construct a quadratic polynomial on unstructured meshes. By differentiating the candidate polynomial, the quadratic terms are obtained by the least-squares method using the average gradient values of the cell itself and its neighboring cells. The linear terms of the polynomial are also determined by the least-squares method. On three-dimensional unstructured meshes, a 3×3 coefficient matrix must be stored, and four least-squares procedures are required to construct a quadratic polynomial. To suppress numerical oscillations in flows with discontinuities, generalized essentially non-oscillatory (GENO) reconstruction and a gradient compression factor are adopted. To accelerate the computation, a multi-GPU accelerated code is implemented using Compute Unified Device Architecture (CUDA) and Message Passing Interface (MPI). The current scheme is fully explicit, and the acceleration framework can be developed based on cell-level parallelism. Numerical examples are presented to evaluate the accuracy and robustness of the scheme, including flows with strong discontinuities, pitching wings, and helicopter rotors. Numerical results confirm the excellent performance of the compact ALE scheme on unstructured meshes.
ER -