Enhanced partial donor cell method for hyperbolic equations in orthogonal curvilinear coordinates

IF 3.4 2区物理与天体物理 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Computer Physics Communications Pub Date : 2025-08-08 DOI:10.1016/j.cpc.2025.109808

Hongyang Luo , Binzheng Zhang , John G. Lyon , Jiaxing Tian

引用次数: 0

Abstract

An enhanced high-order reconstruction method for finite-volume solvers in orthogonal curvilinear coordinates is presented. Extending the classical Partial Donor Method (PDM) to account for geometric effects, the scheme achieves arbitrary high-order convergence while preserving monotonicity and minimizing numerical diffusion. Optimal seventh-order interpolation formulas for uniform cylindrical and spherical-radial grids are derived, complemented by an optional non-clipping algorithm that enhances accuracy near narrow extrema. Extensive tests in both linear and non-linear systems validate the method's high spatial accuracy and non-oscillatory performance. Its straightforward derivation and modest computational overhead render the approach a promising tool for astrophysical, space, and planetary applications, with the potential for extension to other curvilinear systems.

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正交曲线坐标下双曲方程的改进部分供体单元法

提出了一种改进的正交曲线坐标下有限体积解的高阶重构方法。该方案将经典的部分供体方法（PDM）扩展到考虑几何效应，在保持单调性和最小化数值扩散的同时实现任意高阶收敛。推导了均匀圆柱网格和球径向网格的最优七阶插值公式，并辅以可选的非剪切算法，提高了窄极值附近的精度。在线性和非线性系统中的大量测试验证了该方法的高空间精度和非振荡性能。其简单的推导和适度的计算开销使该方法成为天体物理、空间和行星应用的一个有前途的工具，并有可能扩展到其他曲线系统。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Computer Physics Communications 物理-计算机：跨学科应用

CiteScore

12.10

自引率

3.20%

发文量

287

审稿时长

5.3 months

期刊介绍： The focus of CPC is on contemporary computational methods and techniques and their implementation, the effectiveness of which will normally be evidenced by the author(s) within the context of a substantive problem in physics. Within this setting CPC publishes two types of paper. Computer Programs in Physics (CPiP) These papers describe significant computer programs to be archived in the CPC Program Library which is held in the Mendeley Data repository. The submitted software must be covered by an approved open source licence. Papers and associated computer programs that address a problem of contemporary interest in physics that cannot be solved by current software are particularly encouraged. Computational Physics Papers (CP) These are research papers in, but are not limited to, the following themes across computational physics and related disciplines. mathematical and numerical methods and algorithms; computational models including those associated with the design, control and analysis of experiments; and algebraic computation. Each will normally include software implementation and performance details. The software implementation should, ideally, be available via GitHub, Zenodo or an institutional repository.In addition, research papers on the impact of advanced computer architecture and special purpose computers on computing in the physical sciences and software topics related to, and of importance in, the physical sciences may be considered.