Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows

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A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” family ... continued below

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Park, HyeongKae; Nourgaliev, Robert; Mousseau, Vincent & Knoll, Dana July 1, 2008.

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A novel numerical algorithm (rDG-JFNK) for all-speed fluid flows with heat conduction and viscosity is introduced. The rDG-JFNK combines the Discontinuous Galerkin spatial discretization with the implicit Runge-Kutta time integration under the Jacobian-free Newton-Krylov framework. We solve fully-compressible Navier-Stokes equations without operator-splitting of hyperbolic, diffusion and reaction terms, which enables fully-coupled high-order temporal discretization. The stability constraint is removed due to the L-stable Explicit, Singly Diagonal Implicit Runge-Kutta (ESDIRK) scheme. The governing equations are solved in the conservative form, which allows one to accurately compute shock dynamics, as well as low-speed flows. For spatial discretization, we develop a “recovery” family of DG, exhibiting nearly-spectral accuracy. To precondition the Krylov-based linear solver (GMRES), we developed an “Operator-Split”-(OS) Physics Based Preconditioner (PBP), in which we transform/simplify the fully-coupled system to a sequence of segregated scalar problems, each can be solved efficiently with Multigrid method. Each scalar problem is designed to target/cluster eigenvalues of the Jacobian matrix associated with a specific physics.

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  • ICCFD5,KOREA,07/07/2008,07/11/2008

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  • Report No.: INL/CON-08-13822
  • Grant Number: DE-AC07-99ID-13727
  • Office of Scientific & Technical Information Report Number: 936630
  • Archival Resource Key: ark:/67531/metadc894415

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  • July 1, 2008

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  • Sept. 27, 2016, 1:39 a.m.

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  • Dec. 8, 2016, 9:11 p.m.

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Park, HyeongKae; Nourgaliev, Robert; Mousseau, Vincent & Knoll, Dana. Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows, article, July 1, 2008; [Idaho Falls, Idaho]. (digital.library.unt.edu/ark:/67531/metadc894415/: accessed December 10, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT Libraries Government Documents Department.