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

Abstract

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.

Authors:
; ; ;
Publication Date:
Research Org.:
Idaho National Laboratory (INL)
Sponsoring Org.:
USDOE
OSTI Identifier:
936630
Report Number(s):
INL/CON-08-13822
TRN: US0805608
DOE Contract Number:  
DE-AC07-99ID-13727
Resource Type:
Conference
Resource Relation:
Conference: ICCFD5,KOREA,07/07/2008,07/11/2008
Country of Publication:
United States
Language:
English
Subject:
22 GENERAL STUDIES OF NUCLEAR REACTORS; ACCURACY; ALGORITHMS; DIFFUSION; EIGENVALUES; FLUID FLOW; NAVIER-STOKES EQUATIONS; PHYSICS; SCALARS; STABILITY; VISCOSITY; Newton-Krylov; rDG-JFNK

Citation Formats

Park, HyeongKae, Nourgaliev, Robert, Mousseau, Vincent, and Knoll, Dana. Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows. United States: N. p., 2008. Web.
Park, HyeongKae, Nourgaliev, Robert, Mousseau, Vincent, & Knoll, Dana. Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows. United States.
Park, HyeongKae, Nourgaliev, Robert, Mousseau, Vincent, and Knoll, Dana. Tue . "Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows". United States. https://www.osti.gov/servlets/purl/936630.
@article{osti_936630,
title = {Recovery Discontinuous Galerkin Jacobian-Free Newton-Krylov Method for All-Speed Flows},
author = {Park, HyeongKae and Nourgaliev, Robert and Mousseau, Vincent and Knoll, Dana},
abstractNote = {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.},
doi = {},
journal = {},
number = ,
volume = ,
place = {United States},
year = {2008},
month = {7}
}

Conference:
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