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Enhancing the ABAQUS Thermomechanics Code to Simulate Steady and Transient Fuel Rod Behavior

Description: A powerful multidimensional fuels performance capability, applicable to both steady and transient fuel behavior, is developed based on enhancements to the commercially available ABAQUS general-purpose thermomechanics code. Enhanced capabilities are described, including: UO2 temperature and burnup dependent thermal properties, solid and gaseous fission product swelling, fuel densification, fission gas release, cladding thermal and irradiation creep, cladding irradiation growth , gap heat transfer, and gap/plenum gas behavior during irradiation. The various modeling capabilities are demonstrated using a 2D axisymmetric analysis of the upper section of a simplified multi-pellet fuel rod, during both steady and transient operation. Computational results demonstrate the importance of a multidimensional fully-coupled thermomechanics treatment. Interestingly, many of the inherent deficiencies in existing fuel performance codes (e.g., 1D thermomechanics, loose thermo-mechanical coupling, separate steady and transient analysis, cumbersome pre- and post-processing) are, in fact, ABAQUS strengths.
Date: September 1, 2009
Creator: Williamson, R. L. & Knoll, D. A.
Partner: UNT Libraries Government Documents Department

Solving nonlinear heat conduction problems with multigrid preconditioned Newton-Krylov methods

Description: Our objective is to investigate the utility of employing multigrid preconditioned Newton-Krylov methods for solving initial value problems. Multigrid based method promise better performance from the linear scaling associated with them. Our model problem is nonlinear heat conduction which can model idealized Marshak waves. Here we will investigate the efficiency of using a linear multigrid method to precondition a Krylov subspace method. In effect we will show that a fixed point nonlinear iterative method provides an effective preconditioner for the nonlinear problem.
Date: September 1, 1997
Creator: Rider, W.J. & Knoll, D.A.
Partner: UNT Libraries Government Documents Department

A multigrid Newton-Krylov method for flux-limited radiation diffusion

Description: The authors focus on the integration of radiation diffusion including flux-limited diffusion coefficients. The nonlinear integration is accomplished with a Newton-Krylov method preconditioned with a multigrid Picard linearization of the governing equations. They investigate the efficiency of the linear and nonlinear iterative techniques.
Date: September 1, 1998
Creator: Rider, W. J.; Knoll, D. A. & Olson, G. L.
Partner: UNT Libraries Government Documents Department

Investigation of Newton-Krylov algorithms for low Mach number compressible flow

Description: Fully coupled Newton-Krylov algorithms are used to solve steady speed compressible flow past a backward facing step flow Mach and Reynolds numbers. Various preconditioned Krylov iterative methods are used to solve the linear systems that arise on each Newton step, specifically Lanczos-based and Arnoldi-based algorithms. Several preconditioning strategies are considered to improve the performance of these iterative techniques, including incomplete lower-upper factorization with various levels of fill-in [ILU(k)] and domain based additive and multiplicative Schwarz type preconditioning both with and without overlapping domains. The ILU(K) preconditioners were generally less reliable for lower values of the flow Mach number, and exhibited strong sensitivity to cell ordering. In addition, the parallel nature of the domain based preconditioners is exploited on both a shared memory computer and a distributed system of workstations. Important aspects of the numerical solutions are discussed.
Date: October 1, 1995
Creator: McHugh, P.R.; Knoll, D.A.; Mousseau, V.A. & Hansen, G.A.
Partner: UNT Libraries Government Documents Department

Fully implicit solutions of the benchmark backward facing step problem using finite element discretization and inexact Newton's method

Description: A fully implicit solution algorithm based on Newton's method is used to solve the steady, incompressible Navier-Stokes and energy equations. An efficiently evaluated numerical Jacobian is used to simplify implementation, and mesh sequencing is used to increase the radius of convergence of the algorithm. We employ finite volume discretization using the power law scheme of Patankar to solve the benchmark backward facing step problem defined by the ASME K-12 Aerospace Heat Transfer Committee. LINPACK banded Gaussian elimination and the preconditioned transpose-free quasi-minimal residual (TFQMR) algorithm of Freund are studied as possible linear equation solvers. Implementation of the preconditioned TFQMR algorithm requires use of the switched evolution relaxation algorithm of Mulder and Van Leer to ensure convergence. The preconditioned TFQMR algorithm is more memory efficient than the direct solver, but our implementation is not as CPU efficient. Results show that for the level of grid refinement used, power law differencing was not adequate to yield the desired accuracy for this problem.
Date: January 1, 1992
Creator: McHugh, P.R. & Knoll, D.A.
Partner: UNT Libraries Government Documents Department

Multi-Level iterative methods in computational plasma physics

Description: Plasma physics phenomena occur on a wide range of spatial scales and on a wide range of time scales. When attempting to model plasma physics problems numerically the authors are inevitably faced with the need for both fine spatial resolution (fine grids) and implicit time integration methods. Fine grids can tax the efficiency of iterative methods and large time steps can challenge the robustness of iterative methods. To meet these challenges they are developing a hybrid approach where multigrid methods are used as preconditioners to Krylov subspace based iterative methods such as conjugate gradients or GMRES. For nonlinear problems they apply multigrid preconditioning to a matrix-few Newton-GMRES method. Results are presented for application of these multilevel iterative methods to the field solves in implicit moment method PIC, multidimensional nonlinear Fokker-Planck problems, and their initial efforts in particle MHD.
Date: March 1, 1999
Creator: Knoll, D.A.; Barnes, D.C.; Brackbill, J.U.; Chacon, L. & Lapenta, G.
Partner: UNT Libraries Government Documents Department

Newton-Krylov methods applied to nonequilibrium radiation diffusion

Description: The authors present results of applying a matrix-free Newton-Krylov method to a nonequilibrium radiation diffusion problem. Here, there is no use of operator splitting, and Newton`s method is used to convert the nonlinearities within a time step. Since the nonlinear residual is formed, it is used to monitor convergence. It is demonstrated that a simple Picard-based linearization produces a sufficient preconditioning matrix for the Krylov method, thus elevating the need to form or store a Jacobian matrix for Newton`s method. They discuss the possibility that the Newton-Krylov approach may allow larger time steps, without loss of accuracy, as compared to an operator split approach where nonlinearities are not converged within a time step.
Date: March 10, 1998
Creator: Knoll, D. A.; Rider, W. J. & Olsen, G. L.
Partner: UNT Libraries Government Documents Department

Sensitivity analysis of a nonlinear Newton-Krylov solver for heat transfer with phase change.

Description: Development of a complex metal-casting computer model requires information about how varying the problem parameters affects the results (metal flow and solidification). For example, we would like to know how the last point to solidify or the cooling rate at a given location changes when the physical properties of the metal, boundary conditions, or mold geometry are changed. As a preliminary step towards a complete sensitivity analysis of a three-dimensional casting simulation, we examine a one-dimensional version of a metal-alloy phase-change conductive-heat-transfer model by means of Automatic Differentiation (AD). This non-linear 'Jacobian-free' method is a combination of an outer Newton-based iteration and an inner conjugate gradient-like (Krylov) iteration. The implicit solution algorithm has enthalpy as the dependent variable from which temperatures are determined. We examine the sensitivities of the difference between an exact analytical solution for the final temperature and that produced by this algorithm to the problem parameters. In all there are 17 parameters (12 physical constants such as liquid density, heat capacity, and thermal conductivity, 2 initial and boundary condition parameters, the final solution time, and 2 algorithm tolerances). We apply AD in the forward and reverse mode and verify the sensitivities by means of finite differences. In general, the finite-difference method requires at least N+1 computer runs to determine sensitivities for N problem parameters. By forward and reverse, we mean the direction through the solution and in time and space in which the derivative values are obtained. The forward mode is typically more efficient for determining the sensitivity of many responses to one or a few parameters, while the reverse mode is better suited for sensitivities of one or a few responses with respect to many parameters. The sensitivities produced by all the methods agreed to at least three significant figures. The forward and reverse AD code ...
Date: January 1, 2002
Creator: Henninger, Rudolph J.; Knoll, D. A. (Dana A.); Kothe, D. B. (Douglas B.) & Lally, B. R. (Bryan R.)
Partner: UNT Libraries Government Documents Department

Models and applications of the UEDGE code

Description: The transport of particles and energy from the core of a tokamak to nearby material surfaces is an important problem for understanding present experiments and for designing reactor-grade devices. A number of fluid transport codes have been developed to model the plasma in the edge and scrape-off layer (SOL) regions. This report will focus on recent model improvements and illustrative results from the UEDGE code. Some geometric and mesh considerations are introduced, followed by a general description of the plasma and neutral fluid models. A few comments on computational issues are given and then two important applications are illustrated concerning benchmarking and the ITER radiative divertor. Finally, we report on some recent work to improve the models in UEDGE by coupling to a Monte Carlo neutrals code and by utilizing an adaptive grid.
Date: September 1, 1996
Creator: Rensink, M.E.; Knoll, D.A.; Porter, G.D.; Rognlien, T.D.; Smith, G.R. & Wising, F.
Partner: UNT Libraries Government Documents Department

Techniques and results of tokamak-edge simulation

Description: This paper describes recent development of the UEDGE code in three important areas. (1) Non-orthogonal grids allow accurate treatment of experimental geometries in which divertor plates intersect flux surfaces at oblique angles. (2) Radating impurities are included by means of one or more continuity equations that describe transport and sources, and sinks due to ionization and recombination processes. (3) Advanced iterative methods that reduce storage and execution time allow us to find fully converged solutions of larger problems (i.e., finer grids). Sample calculations are presented to illustrate these development.
Date: May 20, 1994
Creator: Smith, G.R.; Brown, P.N.; Rensink, M.E.; Rognlien, T.D.; Campbell, R.B.; Knoll, D.A. et al.
Partner: UNT Libraries Government Documents Department