Parallel Algorithms and Software for Nuclear, Energy, and Environmental Applications. Part I: Multiphysics Algorithms

There is a growing trend within energy and environmental simulation to consider tightly coupled solutions to multiphysics problems. This can be seen in nuclear reactor analysis where analysts are interested in coupled flow, heat transfer and neutronics, and in nuclear fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry. In energy and environmental applications, energy extraction involves geomechanics, flow through porous media and fractured formations, adding heat transport for enhanced oil recovery and geothermal applications, and adding reactive transport in the case of applications modeling the underground flow of contaminants. These more ambitious simulations usually motivate some level of parallel computing. Many of the physics coupling efforts to date utilize simple code coupling or first-order operator splitting, often referred to as loose coupling. While these approaches can produce answers, they usually leave questions of accuracy and stability unanswered. Additionally, the different physics often reside on distinct meshes and data are coupled via simple interpolation, again leaving open questions of stability and accuracy. This paper is the first part of a two part sequence on multiphysics algorithms and software. Part I examines the importance of accurate time and space integration and that the degree of coupling used for the solution should match the requirements of the simulation. It then discusses the preconditioned Jacobian-free Newton Krylov solution algorithm that is used for both multiphysics and multiscale solutions. Part II [1] presents the software framework; the Multiphysics Object Oriented Simulation Environment (MOOSE) and discusses applications based on it.