Glen Hansen

Fully-coupled engineering and mesoscale simulations of thermal conductivity in UO2 fuel using an implicit multiscale approach

Though the thermal conductivity of solid UO2 is well characterized, its value is sensitive to microstructure changes. In this study, we propose a two-way coupling of a mesoscale phase field irradiation model to an engineering scale, finite element calculation to capture the microstructure dependence of the conductivity. To achieve this, the engineering scale thermomechanics system is solved in a parallel, fully-coupled, fully-implicit manner using the preconditioned Jacobian-free Newton Krylov (JFNK) method. Within the JFNK function evaluation phase of the calculation, the microstructure-influenced thermal conductivity is calculated by the mesoscale model and passed back to the engineering scale calculation. Initial results illustrate quadratic nonlinear convergence and good parallel scalability.

Parallel multiphysics algorithms and software for computational nuclear engineering

There is a growing trend in nuclear reactor simulation to consider multiphysics problems. This can be seen in reactor analysis where analysts are interested in coupled flow, heat transfer and neutronics, and in fuel performance simulation where analysts are interested in thermomechanics with contact coupled to species transport and chemistry. These more ambitious simulations usually motivate some level of parallel computing. Many of the 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 separate grids which are coupled via simple interpolation, again leaving open questions of stability and accuracy. Utilizing state of the art mathematics and software development techniques we are deploying next generation tools for nuclear engineering applications. The Jacobian-free Newton-Krylov (JFNK) method combined with physics-based preconditioning provide the underlying mathematical structure for our tools. JFNK is understood to be a modern multiphysics algorithm, but we are also utilizing its unique properties as a scale bridging algorithm. To facilitate rapid development of multiphysics applications we have developed the Multiphysics Object-Oriented Simulation Environment (MOOSE). Examples from two MOOSE-based applications: PRONGHORN, our multiphysics gas cooled reactor simulation tool and BISON, our multiphysics, multiscale fuel performance simulation tool will be presented.

A Jacobian-free Newton Krylov method for mortar-discretized thermomechanical contact problems

Multibody contact problems are common within the field of multiphysics simulation. Applications involving thermomechanical contact scenarios are also quite prevalent. Such problems can be challenging to solve due to the likelihood of thermal expansion affecting contact geometry which, in turn, can change the thermal behavior of the components being analyzed. This paper explores a simple model of a light water reactor nuclear fuel rod, which consists of cylindrical pellets of uranium dioxide (UO2) fuel sealed within a Zircalloy cladding tube. The tube is initially filled with helium gas, which fills the gap between the pellets and cladding tube. The accurate modeling of heat transfer across the gap between fuel pellets and the protective cladding is essential to understanding fuel performance, including cladding stress and behavior under irradiated conditions, which are factors that affect the lifetime of the fuel. The thermomechanical contact approach developed here is based on the mortar finite element method, where Lagrange multipliers are used to enforce weak continuity constraints at participating interfaces. In this formulation, the heat equation couples to linear mechanics through a thermal expansion term. Lagrange multipliers are used to formulate the continuity constraints for both heat flux and interface traction at contact interfaces. The resulting system of nonlinear algebraic equations are cast in residual form for solution of the transient problem. A Jacobian-free Newton Krylov method is used to provide for fully-coupled solution of the coupled thermal contact and heat equations.

Comparison of multimesh hp-FEM to interpolation and projection methods for spatial coupling of thermal and neutron diffusion calculations

Multiphysics solution challenges are legion within the ?eld of nuclear reactor design and analysis. One major issue concerns the coupling between heat and neutron ?ow (neutronics) within the reactor assembly. These phenomena are usually very tightly interdependent, as large amounts of heat are quickly produced with an increase in ?ssion events within the fuel, which raises the temperature that a?ects the neutron cross section of the fuel. Furthermore, there typically is a large diversity of time and spatial scales between mathematical models of heat and neutronics. Indeed, the di?erent spatial resolution requirements often lead to the use of very di?erent meshes for the two phenomena. As the equations are coupled, one must take care in exchanging solution data between them, or signi?cant error can be introduced into the coupled problem. We propose a novel approach to the discretization of the coupled problem on di?erent meshes based on an adaptive multimesh higher-order ?nite element method (hp-FEM), and compare it to popular interpolation and projection methods. We show that the multimesh hp-FEM method is signi?cantly more accurate than the interpolation and projection approaches considered in this study.

The role of data transfer on the selection of a single vs. multiple mesh architecture for tightly coupled multiphysics applications

Data transfer from one distinct mesh to another may be necessary in any number of applications, including prolongation operations supporting multigrid solution methods, spatial adaptation, remeshing, and arbitrary Lagrangian-Eulerian (ALE) and multiphysics simulation. This data transfer process is also referred to as remapping, rezoning and interpolation. Intermesh data transfer has the potential to introduce error into a simulation; the magnitude and importance of which depends on the transfer scenario and the algorithm used to perform the transfer. For a transient analysis, data transfer may occur many times during a simulation, with possible error accumulation at each transfer. The present study develops selected scenarios that illustrate data transfer error and how it might impact an analysis. This study examines remapping error by using static analytical functions to compare various remapping schemes. It also investigates the significance and nature of data transfer error for a simple multiphysics system involving a transient coupled system of partial differential equations. It concludes that remapping error can be significant both for static functions and for coupled multiphysics systems. Aggregate error is shown to be a function of remapping scheme, mesh coarseness, nature of the remapped function and mesh disparity. In cases of extreme mesh disparity, thismorexa0» study shows that remapping can lead to excessive error and even to solution instability. Further, this work motivates that remapping error should be included in the estimation of numerical error, if data transfer is employed in a numerical simulation.«xa0less

Quasi-Orthogonal Grids with Impedance Matching

An elliptic, quasi-orthogonal grid generation system is formulated based on quasi-conformal mapping for arbitrary anisotropic (long and skinny) regions. The resulting system is a generalization of the well-known elliptic grid generation system derived from conformal mapping. Coupled with the grid generation system, the impedance-matching principle describes a methodology for preserving the discrete accuracy of the simulation, both internal to the domain and near internal geometric interfaces. Empirically, satisfying the impedance principle tends to minimize mesh effects on the solution results; meshes that are impedance-matched tend to reduce or eliminate spurious wave reflection and/or attenuation at internal interfaces. The resulting grid generation system is used to construct impedance-matched quasi-orthogonal grids on domains containing internal geometric constraints given an algebraic grid and a grid impedance function as initial conditions.

Efficient nonlinear solvers for Laplace-Beltrami smoothing of three-dimensional unstructured grids

The Laplace-Beltrami system of nonlinear, elliptic, partial differential equations has utility in the generation of computational grids on complex and highly curved geometry. Discretization of this system using the finite-element method accommodates unstructured grids, but generates a large, sparse, ill-conditioned system of nonlinear discrete equations. The use of the Laplace-Beltrami approach, particularly in large-scale applications, has been limited by the scalability and efficiency of solvers. This paper addresses this limitation by developing two nonlinear solvers based on the Jacobian-Free Newton-Krylov (JFNK) methodology. A key feature of these methods is that the Jacobian is not formed explicitly for use by the underlying linear solver. Iterative linear solvers such as the Generalized Minimal RESidual (GMRES) method do not technically require the stand-alone Jacobian; instead its action on a vector is approximated through two nonlinear function evaluations. The preconditioning required by GMRES is also discussed. Two different preconditioners are developed, both of which employ existing Algebraic Multigrid (AMG) methods. Further, the most efficient preconditioner, overall, for the problems considered is based on a Picard linearization. Numerical examples demonstrate that these solvers are significantly faster than a standard Newton-Krylov approach; a speedup factor of approximately 26 was obtained for the Picard preconditioner on the largest grids studied here. In addition, these JFNK solvers exhibit good algorithmic scaling with increasing grid size.

Unstructured surface mesh adaptation using the Laplace-Beltrami target metric approach

This paper develops a set of adaptive surface mesh equations by using a harmonic morphism, which is a special case of a harmonic map. These equations are applicable both to structured and unstructured surface meshes, provided that the underlying surface is given in a parametric form. By representing the target metric of the mesh as a sum of a coarse-grained component and a component quadratic in surface gradients, an improved surface mesh may be obtained. The weak form of the grid equations is solved using the finite element approximation, which reduces the grid equations to a nonlinear, algebraic set. Examples of structured and unstructured meshes are used to illustrate the applicability of the proposed approach.