Publications

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Time integration is a central component for most transient simulations. It coordinates many of the major parts of a simulation together, e.g., a residual calculation with a transient solver, solution with the output, various operator-split physics, and forward and adjoint solutions for inversion. Even though there is this variety in these transient simulations, there is still a common set of algorithms and procedures to progress transient solutions for ordinary-differential equations (ODEs) and differential-alegbraic equations (DAEs). Rythmos is a collection of these algorithms that can be used for the solution of transient simulations. It provides common time-integration methods, such as Backward and Forward Euler, Explicit and Implicit Runge-Kutta, and Backward-Difference Formulas. It can also provide sensitivities, and adjoint components for transient simulations. Rythmos is a package within Trilinos, and requires some other packages (e.g., Teuchos and Thrya) to provide basic time-integration capabilities. It also can be coupled with several other Trilinos packages to provide additional capabilities (e.g., AztecOO and Belos for linear solutions, and NOX for non-linear solutions). The documentation is broken down into three parts: Theory Manual, User's Manual, and Developer's Guide. The Theory Manual contains the basic theory of the time integrators, the nomenclature and mathematical structure utilized within Rythmos, and verification results demonstrating that the designed order of accuracy is achieved. The User's Manual provides information on how to use the Rythmos, description of input parameters through Teuchos Parameter Lists, and description of convergence test examples. The Developer's Guide is a high-level discussion of the design and structure of Rythmos to provide information to developers for the continued development of capabilities. Details of individual components can be found in the Doxygen webpages.

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A critical aspect of applying modern computational solution methods to complex multiphysics systems of relevance to nuclear reactor modeling, is the assessment of the predictive capability of specific proposed mathematical models. In this respect the understanding of numerical error, the sensitivity of the solution to parameters associated with input data, boundary condition uncertainty, and mathematical models is critical. Additionally, the ability to evaluate and or approximate the model efficiently, to allow development of a reasonable level of statistical diagnostics of the mathematical model and the physical system, is of central importance. In this study we report on initial efforts to apply integrated adjoint-based computational analysis and automatic differentiation tools to begin to address these issues. The study is carried out in the context of a Reynolds averaged Navier-Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods. Initial results are presented that show the promise of these computational techniques in the context of nuclear reactor relevant prototype thermal-hydraulics problems.

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The computational solution of the governing balance equations for mass, momentum, heat transfer and magnetic induction for resistive magnetohydrodynamics (MHD) systems can be extremely challenging. These difficulties arise from both the strong nonlinear, nonsymmetric coupling of fluid and electromagnetic phenomena, as well as the significant range of time- and length-scales that the interactions of these physical mechanisms produce. This paper explores the development of a scalable, fully-implicit stabilized unstructured finite element (FE) capability for 3D incompressible resistive MHD. The discussion considers the development of a stabilized FE formulation in context of the variational multiscale (VMS) method, and describes the scalable implicit time integration and direct-to-steady-state solution capability. The nonlinear solver strategy employs Newton-Krylov methods, which are preconditioned using fully-coupled algebraic multilevel preconditioners. These preconditioners are shown to enable a robust, scalable and efficient solution approach for the large-scale sparse linear systems generated by the Newton linearization. Verification results demonstrate the expected order-of-accuracy for the stabilized FE discretization. The approach is tested on a variety of prototype problems, that include MHD duct flows, an unstable hydromagnetic Kelvin-Helmholtz shear layer, and a 3D island coalescence problem used to model magnetic reconnection. Initial results that explore the scaling of the solution methods are also presented on up to 128K processors for problems with up to 1.8B unknowns on a CrayXK7.

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This paper evaluates the performance of multiphysics coupling algorithms applied to a light water nuclear reactor core simulation. The simulation couples the k-eigenvalue form of the neutron transport equation with heat conduction and subchannel flow equations. We compare Picard iteration (block Gauss-Seidel) to Anderson acceleration and multiple variants of preconditioned Jacobian-free Newton-Krylov (JFNK). The performance of the methods are evaluated over a range of energy group structures and core power levels. A novel physics-based approximation to a Jacobian-vector product has been developed to mitigate the impact of expensive on-line cross section processing steps. Numerical simulations demonstrating the efficiency of JFNK and Anderson acceleration relative to standard Picard iteration are performed on a 3D model of a nuclear fuel assembly. Both criticality (k-eigenvalue) and critical boron search problems are considered.

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As the Consortium for Advanced Simulation of Light Water Reactors (CASL) moves forward with more complex multiphysics simulations, there is increased focus on incorporating fuel performance analysis methods. The coupled neutronics/thermal-hydraulics capabilities within the Virtual Environment for Reactor Applications Core Simulator (VERA-CS) have become relatively stable and major advances have been made in analysis efforts, including the simulations of twelve cycles of Watts Bar Nuclear Unit 1 (WBN1) operation. However, VERA-CS approaches for treating fuel pin heat transfer have well-known limitations that could be eliminated through better integration with the BISON-CASL fuel performance code. Several approaches are being taken to improve or replace the VERA-CS fuel models and improve integration with BISON-CASL. Tiamat is being developed to replace the fuel models with a direct coupling of BISON-CASL and the neutronics and coolant heat transfer of VERA-CS. Tiamat will execute in an inline mode that allows for in-memory transfer of VERA-CS data to BISON-CASL. This will provide fuel performance results during core simulation. However, fuel performance typically undergoes an independent analysis using a stand-alone fuel performance code with manually specified input defined from an independent core simulator solution or set of assumptions. This milestone covers initial efforts to facilitate using VERA for core simulation and fuel performance to operate in this mode of execution. This approach will be used for several CASL fuel performance challenges, such as RIAs and DNB. These issues require time-dependent full core results to establish the boundary conditions for the high-fidelity BISON-CASL simulations. The approach will also be used to improve fuel temperature models in VERA-CS, guide the development of Tiamat, and simplify the use of BISON-CASL within VERA for industry users.