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标量守恒律的精确粒子方法及其在刚性反应动力学中的应用

An exact particle method for scalar conservation laws and its application to stiff reaction kinetics

G. Millán Institute of Fluid Dynamics Nanoscience and Industrial Mathematics University Carlos III de Madrid（卡洛斯三世大学G.米兰流体力学纳米科学与工业数学研究所）；Department of Mathematics Temple University（天普大学数学系）

Yossi Farjoun, Benjamin Seibold

备注：
14 page, 7 figures, presented in the Fifth International Workshop on Meshfree Methods for Partial Differential Equations
发表信息：
Meshfree methods for Partial Differential Equations V, Lecture Notes in Computational Science and Engineering, Vol. 79, Griebel, M. and Schweitzer, M.A. (ed.), Springer, 2011, pp. 105-124
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AI总结：

提出一种基于激波粒子和局部相似解的精确粒子方法，用于标量一维双曲守恒律，并扩展至刚性平衡律，无需解析内部动力学即可正确演化爆轰波速度。

摘要：

提出了一种标量一维双曲守恒律的“精确”方法。该方法基于激波粒子的演化，由局部相似解分隔。数值解处处定义，其精度与应用ODE求解器的精度相同。此外，该方法被扩展到刚性平衡律。一种特殊的校正方法产生了一种方法，该方法以正确的速度演化爆轰波，而无需解析其内部动力学。在数值精度方面，将粒子方法与经典有限体积法进行了比较，既针对守恒律，也针对反应动力学中的应用。

英文摘要：

An "exact" method for scalar one-dimensional hyperbolic conservation laws is presented. The approach is based on the evolution of shock particles, separated by local similarity solutions. The numerical solution is defined everywhere, and is as accurate as the applied ODE solver. Furthermore, the method is extended to stiff balance laws. A special correction approach yields a method that evolves detonation waves at correct velocities, without resolving their internal dynamics. The particle approach is compared to a classical finite volume method in terms of numerical accuracy, both for conservation laws and for an application in reaction kinetics.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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