Approaches for mitigating over‐solving in multiphysics simulations

Abstract

Summary Multiphysics simulations are used to solve coupled physics problems found in a wide variety of applications in natural and engineering systems. Combining models of different physical processes into one computational tool is the essence of multiphysics simulation. A general and widely used coupling approach is to combine several ‘single‐physics’ numerical solvers, each already being well developed, mature/sophisticated into an iteration‐based computational package. This approach iterates over the constituent solvers at every time step, to obtain globally converged solutions. During the simulation, each single‐physics component is solved repeatedly until the feedback has been adequately resolved. However, the component problem solution only needs to be as precise as the feedback that it receives from the other component. Thus, computational effort expended to exceed such precision is wasted. This issue is usually called over‐solving. This paper proposes and discusses several methods that circumvent over‐solving. The residual balance, relaxed relative tolerance, alternating nonlinear, and solution interruption methods are described, and their performance is compared with Picard iteration. A steady state problem with coupling along an interface and a transient problem with two fields coupled throughout the spatial domain are solved as examples. These problems demonstrate that the savings associated with eliminating over‐solving can reach at least 30% without any loss in accuracy. Copyright © 2017 John Wiley & Sons, Ltd.

Inexact Methods for Sequential Fully Implicit (SFI) Reservoir Simulation

“…In standard SFI, sub-problems are usually solved to high precision at every outer iteration. That over-solving may result in wasted computations contributing little progress towards the coupled solution (Dembo et al 1982;Eisenstat and Walker 1996;Senecal and Ji 2017). To demonstrate this issue, we examine a test case described in Section 6.1, which is a two-dimensional gravity-driven two-phase problem.…”

“…inner) iterations are controlled in a way that the Newton (i.e. outer) convergence is not degraded, but overall computational efforts are largely decreased (Senecal and Ji 2017). Next we present three options of inexact methods for SFI.…”

“…It is found that, however, there is no need for one sub-problem to strive for perfection ('over-solving'), while the coupled (outer) residual remains high due to the other sub-problem. Over-solving may result in wasted computations that contribute little or no progress towards the coupled solution (Dembo et al 1982;Eisenstat and Walker 1996;Senecal and Ji 2017). Our objective here is to minimize the cost of inner solvers while not degrading the convergence rate of SFI.…”

Multi-physics coupling simulation in virtual reactors

“…23 One alternative coupling strategy is to describe all related physical models into one set of equations, and often a Newton-based method such as the JFNK method is applied to solve the equations. 25,26 Compared to OS and the Picard iteration, the JFNK method is a tighter and more accurate coupling strategy. The JFNK method solves the physics-related equations (usually PDEs) simultaneously, and simulates multiple physical processes in a monolithic code.…”

“…Great efforts have been made in the research toward the multi-physics coupling. 25,[39][40][41][42][43][44][45][46] In this section, we discuss some coupling software in several representative virtual reactor projects.…”