Hybrid Surface Mesh Adaptation for Climate Modeling

Solution-driven mesh adaptation is becoming quite popular for spatial error control in the numerical simulation of complex computational physics applications,such as climate modeling.Typically,spatial adaptation is achieved by element subdivision (h adaptation) with a primary goal of resolving the local length scales of interest.A sec- ond,less-popular method of spatial adaptivity is called'mesh motion'(r adaptation); the smooth repositioning of mesh node points aimed at resizing existing elements to capture the local length scales.This paper proposes an adaptation method based on a combination of both element subdivision and node point repositioning (rh adaptation). By combining these two methods using the notion of a mobility function,the proposed approach seeks to increase the flexibility and extensibility of mesh motion algorithms while providing a somewhat smoother transition between refined regions than is pro- duced by element subdivision alone.Further,in an attempt to support the requirements of a very general class of climate simulation applications,the proposed method is de- signed to accommodate unstructured,polygonal mesh topologies in addition to the most popular mesh types.

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

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 applicationmust also take care tominimize 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-freeNewton-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.

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.∗Corresponding author.Email addresses:Derek.Gaston@inl.gov(D.Gaston),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.