A review of structure-preserving numerical methods for engineering applications
A review of structure-preserving numerical methods for engineering applications
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DOI：
10.1016/j.cma.2020.113067
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发表时间：
2020-07
影响因子：
7.2
通讯作者：
Harsh Sharma;M. Patil;C. Woolsey
中科院分区：
文献类型：
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作者：
Harsh Sharma;M. Patil;C. Woolsey
动力系统的精确数值模拟在从粒子物理到地球物理流体流动到空间灾害分析的应用中是必不可少的。然而，大多数传统的数值方法不考虑物理系统的基本几何结构，导致模拟结果可能暗示非物理行为。几何数值积分（GNI）领域关注的是通过保持控制微分方程的几何性质来尊重问题的基本物理的数值方法。过去二十年的研究已经产生了非常准确的GNI方法，现在它们被用于保守动力系统长期模拟的基准测试。然而，它们在大规模工程问题中的效用仍然是一个悬而未决的问题。本文对保结构数值方法的工程应用进行了综述。本文的目的是提供一个概述不同类别的GNI方法的机械系统，同时提供一个调查的实际例子，从数值模拟的现实工程问题。
Accurate numerical simulation of dynamical systems is essential in applications ranging from particle physics to geophysical fluid flow to space hazard analysis. However, most traditional numerical methods do not account for the underlying geometric structure of the physical system, leading to simulation results that may suggest nonphysical behavior. The field of geometric numerical integration (GNI) is concerned with numerical methods that respect the fundamental physics of a problem by preserving the geometric properties of the governing differential equations. Research over the past two decades has produced GNI methods that are so accurate that they are now used for benchmarking purposes for long-time simulation of conservative dynamical systems. However, their utility for large-scale engineering problems is still an open question. This paper presents a review of structure-preserving numerical methods with focus on their engineering applications. The purpose of this paper is to provide an overview of different classes of GNI methods for mechanical systems while providing a survey of practical examples from numerical simulation of realistic engineering problems.