论文标题
Navier-Stokes-Fourier System的变分离散化
Variational discretization of the Navier-Stokes-Fourier system
论文作者
论文摘要
本文介绍了可压缩的Navier-Stokes-toury System的变异离散化，其中粘度和热传导项是在一位作者开发的非平衡热力学的变异方法中处理的。在第一部分中，我们回顾了平滑设置中Navier-Stokes-Fourier（NSF）系统的变分框架。在第二部分中，我们通过使用此离散的外部积分来审查基于离散的差异性的离散外观演算，然后继续为NSF系统建立空间离散的变异原理，从而产生半差异的非差异原理，以及半差异原理。为了避免重要的技术困难，需要对现象学约束进行进一步治疗。在第三部分中，我们通过扩展作者的先前工作来分散NSF系统基础的空间变异原理，该作者终于产生了NSF系统的非外观变分积分器，以及完全离散的进化方程。
This paper presents the variational discretization of the compressible Navier-Stokes-Fourier system, in which the viscosity and the heat conduction terms are handled within the variational approach to nonequilibrium thermodynamics as developed by one of the authors. In a first part, we review the variational framework for the Navier-Stokes-Fourier (NSF) system in the smooth setting. In a second part, we review a discrete exterior calculus based on discrete diffeomorphisms then proceed to establish the spatially discretized variational principle for the NSF system through the use of this discrete exterior calculus, which yields a semi-discrete nonholonomic variational principle, as well as semi-discrete evolution equations. In order to avoid important technical difficulties, further treatment of the phenomenological constraint is needed. In a third part we discretize in time the spatial variational principle underlying the NSF system by extending previous work of the authors, which at last yields a nonholonomic variational integrator for the NSF system, as well as fully discrete evolution equations.
