具有动力学效应动态局域化的多尺度动理学-流体求解器
A Multiscale Kinetic-Fluid Solver with Dynamic Localization of Kinetic Effects
AI总结：
本文基于前期工作构建了一种鲁棒的多尺度动理学-流体求解器，通过微-宏分解和时空依赖的过渡函数，动态定位并修正流体模型中的非平衡区域，并提出了基于分布函数的新判据来定义流体模型的失效条件。
摘要：
本文汇集了我们在前期工作[P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J. Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)]中的努力，以构建一个鲁棒的多尺度动理学-流体求解器。我们的目标是高效求解存在非平衡局域化区域（这些区域可以随时间移动、合并、出现或消失）的流体动力学问题。本文的主要要素如下：在整个计算域上求解流体模型，同时引入局域化的动理学升尺度项，在必要时修正流体模型；通过分布函数的微-宏分解[P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)]获得这种多尺度流动描述；通过时间和空间依赖的过渡函数实现流体描述与动理学描述之间的动态转换；为了高效定义流体模型的失效条件，我们提出了一个基于分布函数本身的新判据。最后给出了多个数值算例以验证该方法并衡量其计算效率。
英文摘要：
This paper collects the efforts done in our previous works [P. Degond, S. Jin, L. Mieussens, A Smooth Transition Between Kinetic and Hydrodynamic Equations, J. Comp. Phys., 209 (2005) 665--694.],[P.Degond, G. Dimarco, L. Mieussens, A Moving Interface Method for Dynamic Kinetic-fluid Coupling, J. Comp. Phys., Vol. 227, pp. 1176-1208, (2007).],[P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)] to build a robust multiscale kinetic-fluid solver. Our scope is to efficiently solve fluid dynamic problems which present non equilibrium localized regions that can move, merge, appear or disappear in time. The main ingredients of the present work are the followings ones: a fluid model is solved in the whole domain together with a localized kinetic upscaling term that corrects the fluid model wherever it is necessary; this multiscale description of the flow is obtained by using a micro-macro decomposition of the distribution function [P. Degond, J.G. Liu, L. Mieussens, Macroscopic Fluid Model with Localized Kinetic Upscaling Effects, SIAM Multi. Model. Sim. 5(3), 940--979 (2006)]; the dynamic transition between fluid and kinetic descriptions is obtained by using a time and space dependent transition function; to efficiently define the breakdown conditions of fluid models we propose a new criterion based on the distribution function itself. Several numerical examples are presented to validate the method and measure its computational efficiency.
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