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A Jacobian-Free Newton Krylov Implicit-Explicit Time Integration Method for Incompressible Flow Problems

Communications in Computational Physics 2013年第5期13卷 1408-1431页

作者： Samet Y.Kadioglu dana a.knoll Department of Mathematical Engineering Yildiz Technical University34210 Davutpasa-EsenlerIstanbulTurkey Fuels Modeling and Simulation Department Idaho National LaboratoryP.O.Box 1625MS 3840Idaho FallsID 83415USA Theoretical Division Los Alamos National LaboratoryP.O.Box 1663MS B-216Los AlamosNM87545USA

We have introduced a fully second order IMplicit/EXplicit(IMEX)time integration technique for solving the compressible Euler equations plus nonlinear heat conduction problems(also known as the radiation hydrodynamics problems)in Kadioglu et al.,***[22,24].In this paper,we study the implications when this method is applied to the incompressible Navier-Stokes(N-S)*** IMEX method is applied to the incompressible flow equations in the following *** hyperbolic terms of the flow equations are solved explicitly exploiting the well understood explicit *** the other hand,an implicit strategy is employed for the non-hyperbolic *** explicit part is embedded in the implicit step in such a way that it is solved as part of the non-linear function evaluation within the framework of the Jacobian-Free Newton Krylov(JFNK)method[8,29,31].This is done to obtain a self-consistent implementation of the IMEX method that eliminates the potential order reduction in time accuracy due to the specific operator *** employ a simple yet quite effective fractional step projection methodology(similar to those in[11,19,21,30])as our preconditioner inside the JFNK *** present results from several test *** each test,we show second order time ***,we present a study for the algorithm performance of the JFNK solver with the new projection method based preconditioner.

关键词： Incompressible flow Navier-Stokes equations IMEX method JFNK method preconditioner

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Parallel Algorithms and Software for Nuclear,Energy,and Environmental *** Ⅱ:Multiphysics Software

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Communications in Computational Physics 2012年第8期12卷 834-865页

作者： Derek Gaston Luanjing Guo Glen Hansen Hai Huang Richard Johnson Dana.knoll Chris Newman Hyeong Kae Park Robert Podgorney Michael Tonks Richard Williamson Nuclear Science and Technology Idaho National LaboratoryIdaho FallsID 83415USA Energy and Environment Science and Technology Idaho National LaboratoryIdaho FallsID 83415USA Multiphysics Simulation Technologies Dept.(1444) Sandia National LaboratoriesAlbuquerqueNM 87185USA Fluid Dynamics and Solid Mechanics Group(T-3) Los Alamos National LaboratoryLos AlamosNM 87545USA.

This paper is the second part of a two part sequence on multiphysics algorithms and *** first[1]focused on the algorithms;this part treats the multiphysics software framework and applications based on *** 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 *** 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 *** paper presents an application framework that was specifically designed to support tightly coupled multiphysics *** 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 *** 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.

关键词： Multiphysics simulation Jacobian-free Newton Krylov finite element applications physics-based preconditioning

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