The role of dimensionless ratios in engineering and physics is ubiquitous; but their utility in the multiphysics community is sometimes overlooked. Notably, in the multiphysics modelling community, coupling methods are often discussed and developed without an explicit monitoring of the various dimensionless ratios of the various inter-physics coupling terms. However, it is evident that the varying strengths of the coupling terms in a multiphysics model of k physics solvers/modules will influence either the convergence rate, the stability of the coupling scheme and the program execution speed. In fact, it is well known that the “ordering” of the predictor physics modules is primordial to the performance characteristics of a multiphysics coupling scheme. However, the question of “how to order” (who came first, the chicken or the egg?) the k physics modules remains vaguely discussed. In fact, physics ordering is generally based on the scientist's experience or on problem specific stability analyses performed on academic computational configurations. In the case of generic multiphysics coupling, where volume, interface and/or surface coupling terms can manifest, the optimal ordering of the physics modules may strongly vary along simulation time (for the same application) and/or across applications. Motivated to find an approximate measure that does not resort to cumbersome and problem specific stability analyses, we borrow the concept of dimensionless numbers from physics and apply it to the algebraic systems that manifest in multiphysics computational models. The “chicken-egg” algorithm is based on a dimensionless methodology that serves to “reorder” the Jacobian matrix of an exact Newton-Raphson implicit scheme. The method poses a dimensionless preconditioner that estimates the different strengths of the various coupling terms found in the multiphysics application. The chicken-egg algorithm estimates at every given time step the order of magnitude of coupling terms and correspondingly orders the k partitioned physics solvers automatically. This algorithm is tested for the first time on a thermo-hygro-corrosive multiphysics model and shows promising results. Benchmarking against monolithic and diagonalised calculation strategies, the first numerical tests show a significant reduction in iterations before convergence and thus over a 1.7-fold improvement in program execution time.

中文翻译：

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跨物理场耦合强度的动态表征，一种为多物理场应用耦合和重新排序分区求解器的方法


无量纲比在工程和物理学中的作用无处不在;但它们在多物理场社区中的实用性有时会被忽视。值得注意的是，在多物理场建模社区中，经常讨论和开发耦合方法，而没有明确监控各种物理场间耦合项的各种无量纲比。然而，很明显，在 k 个物理求解器/模块的多物理场模型中，耦合项的不同强度会影响收敛速率、耦合方案的稳定性和程序执行速度。事实上，众所周知，预测器物理模块的 “排序” 是多物理场耦合方案性能特征的首要因素。然而，k 物理模块的“如何排序”（谁先来，先有鸡还是先有蛋？）的问题仍然被模糊地讨论。事实上，物理学排序通常基于科学家的经验或对学术计算配置执行的特定问题稳定性分析。在通用多物理场耦合的情况下，体积、界面和/或表面耦合项可以表现出来，物理场模块的最佳顺序可能会随着仿真时间（对于同一应用程序）和/或不同应用程序而有很大差异。为了找到一种不求助于繁琐且特定于问题的稳定性分析的近似度量，我们从物理学中借用了无量纲数的概念，并将其应用于多物理场计算模型中体现的代数系统。“先有鸡先有蛋”算法基于无量纲方法，该方法用于“重新排序”精确 Newton-Raphson 隐式方案的雅可比矩阵。 该方法提出了一个无量纲预调节器，用于估计多物理场应用中各种耦合项的不同强度。先有鸡还是先有蛋算法在每个给定的时间步长估计耦合项的数量级，并相应地自动对 k 个分区的物理求解器进行排序。该算法首次在热-湿-腐蚀多物理场模型上进行了测试，并显示出有希望的结果。以整体和对角化计算策略为基准，第一个数值测试显示，收敛前的迭代次数显著减少，因此程序执行时间缩短了 1.7 倍以上。