Dynamic characterization of cross-physics coupling strengths, a methodology to coupling and reordering partitioned solvers for multiphysics applications

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.