论文标题
用于热传导粘性流体的变分和热力学一致性有限元离散化
Variational and thermodynamically consistent finite element discretization for heat conducting viscous fluids
论文作者
论文摘要
尊重热力学定律对于确保动态系统的数值模拟带来物理相关的结果至关重要。在本文中，我们用一般状态方程构建了一种具有结构性和热力学一致的有限元方法和时间稳定的方案。该方法是通过离散的非平衡热力学的变分配方来推导的，该公式将汉密尔顿的流体原理扩展到具有不可逆过程的系统。所得的方案在空间和时间离散的水平上保留了能量和质量与机器精度以及热力学的第二定律的平衡。该方法证明该方法同时适用于绝缘和规定的热通量边界条件以及规定的温度边界条件。我们用Rayleigh-Bénard热对流说明了该方案的特性。虽然重点是进行粘性流体，但提出的离散变异框架为连续体系统的热力学一致离散化的系统构建铺平了道路。
Respecting the laws of thermodynamics is crucial for ensuring that numerical simulations of dynamical systems deliver physically relevant results. In this paper, we construct a structure-preserving and thermodynamically consistent finite element method and time-stepping scheme for heat conducting viscous fluids, with general state equations. The method is deduced by discretizing a variational formulation for nonequilibrium thermodynamics that extends Hamilton's principle for fluids to systems with irreversible processes. The resulting scheme preserves the balance of energy and mass to machine precision, as well as the second law of thermodynamics, both at the spatially and temporally discrete levels. The method is shown to apply both with insulated and prescribed heat flux boundary conditions, as well as with prescribed temperature boundary conditions. We illustrate the properties of the scheme with the Rayleigh-Bénard thermal convection. While the focus is on heat conducting viscous fluids, the proposed discrete variational framework paves the way to a systematic construction of thermodynamically consistent discretizations of continuum systems.
