This paper is the second part of a two part sequence on multiphysics algorithms and software. The first [1] focused on the algorithms; this part treats the multiphysics software framework and applications based on it. Tight coupling is typically designed into the analysis application at inception, as such an application is strongly tied to a composite nonlinear solver that arrives at the final solution by treating all equations simultaneously. The application must also take care to minimize both time and space error between the physics, particularly if more than one mesh representation is needed in the solution process. This paper presents an application framework that was specifically designed to support tightly coupled multiphysics analysis. The Multiphysics Object Oriented Simulation Environment (MOOSE) is based on the Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning to provide the underlying mathematical structure for applications. The report concludes with the presentation of a host of nuclear, energy and environmental applications that demonstrate the efficacy of the approach and the utility of a well-designed multiphysics framework.

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.