Thermodynamically consistent time‐stepping algorithms for non‐linear thermomechanical systems
Thermodynamically consistent time‐stepping algorithms for non‐linear thermomechanical systems
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DOI：
10.1002/nme.2588
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发表时间：
2009-08
影响因子：
2.9
通讯作者：
I. Romero
中科院分区：
文献类型：
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作者：
I. Romero
我们提出了发展新的单片和交错时间步进算法的基本理论，用于一般非线性，耦合，热机械问题。所提出的方法在热力学上是一致的，因为它们的解严格遵守热力学的两条定律：对于孤立系统，它们保持总能量，熵从不减少。此外，如果问题的控制方程具有对称性，所提出的积分器也能保持对称性。这种方法的表述基于两个思想：用所谓的非平衡可逆不可逆耦合的一般方程来表示演化方程，并从一开始就在离散向量场上施加一定的方向性和退化条件。新方法可以看作是能量-动量积分算法在耦合热-力学问题上的扩展，在纯哈密顿情况下，它们可以简化为耦合热-力学问题。本文将这些新思想应用于一个简单的耦合问题：对称的双热弹性摆。数值模拟验证了所提出方法的定性特征，并说明了它们出色的数值稳定性，这正是由于它们能够保持它们离散化的演化方程的结构。版权所有©2009 John Wiley & Sons， Ltd
We present the basic theory for developing novel monolithic and staggered time‐stepping algorithms for general non‐linear, coupled, thermomechanical problems. The proposed methods are thermodynamically consistent in the sense that their solutions rigorously comply with the two laws of thermodynamics: for isolated systems they preserve the total energy and the entropy never decreases. Furthermore, if the governing equations of the problem have symmetries, the proposed integrators preserve them too. The formulation of such methods is based on two ideas: expressing the evolution equation in the so‐called General Equations for Non‐Equilibrium Reversible Irreversible Coupling format and enforcing from their inception certain directionality and degeneracy conditions on the discrete vector fields. The new methods can be considered as an extension of the energy–momentum integration algorithms to coupled thermomechanical problems, to which they reduce in the purely Hamiltonian case. In the article, the new ideas are applied to a simple coupled problem: a double thermoelastic pendulum with symmetry. Numerical simulations verify the qualitative features of the proposed methods and illustrate their excellent numerical stability, which stems precisely from their ability to preserve the structure of the evolution equations they discretize. Copyright © 2009 John Wiley & Sons, Ltd.