Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

Song Gao; Wagdi G. Habashi; Marco Fossati; Dario Isola; Guido S. Baruzzi

doi:10.2514/6.2017-0085

Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

Song Gao, Wagdi G. Habashi, Marco Fossati, Dario Isola, Guido S. Baruzzi

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution book

6 Citations (Scopus)

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Abstract

A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

Original language	English
Title of host publication	55th AIAA Aerospace Sciences Meeting
Place of Publication	Grapevine, Texas
Pages	1-28
Number of pages	28
ISBN (Electronic)	9781624104473
DOIs	https://doi.org/10.2514/6.2017-0085
Publication status	Published - 5 Jan 2017
Event	55th AIAA Aerospace Sciences Meeting - Grapevine, United States Duration: 9 Jan 2017 → 13 Jan 2017 http://scitech.aiaa.org/asm/

Publication series

Name	AIAA SciTech Forum
Publisher	American Institute of Aeronautics and Astronautics

Conference

Conference	55th AIAA Aerospace Sciences Meeting
Abbreviated title	AIAA SciTech 2017
Country/Territory	United States
City	Grapevine
Period	9/01/17 → 13/01/17
Internet address	http://scitech.aiaa.org/asm/

Keywords

Jacobian-free
solvers
supersonic
viscous flows
hybrid grids
finite element
spatial discretization
Newton-Krylov method

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Gao-etal-AIAA-Aerospace-Sciences-Meeting-2017-Finite-element-formulation-of-a-jacobian-free-solverAccepted author manuscript, 2.99 MB

Cite this

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title = "Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids",

abstract = "A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.",

keywords = "Jacobian-free, solvers, supersonic, viscous flows, hybrid grids, finite element, spatial discretization, Newton-Krylov method",

author = "Song Gao and Habashi, {Wagdi G.} and Marco Fossati and Dario Isola and Baruzzi, {Guido S.}",

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year = "2017",

month = jan,

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doi = "10.2514/6.2017-0085",

language = "English",

series = "AIAA SciTech Forum",

publisher = "American Institute of Aeronautics and Astronautics",

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T1 - Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

AU - Gao, Song

AU - Habashi, Wagdi G.

AU - Fossati, Marco

AU - Isola, Dario

AU - Baruzzi, Guido S.

N1 - ©2017 AIAA Song Gao, Wagdi G. Habashi, Marco Fossati, and Dario Isola. and Guido S. Baruzzi. "Finite-Element Formulation of a Jacobian-free Solver for Supersonic Viscous Flows on Hybrid Grids", 55th AIAA Aerospace Sciences Meeting, AIAA SciTech Forum, (AIAA 2017-1627) https://doi.org/10.2514/6.2017-0085

PY - 2017/1/5

Y1 - 2017/1/5

N2 - A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

AB - A parallel Jacobian-free solver for supersonic flows on unstructured hybrid meshes is proposed. An edge-based Finite Element formulation is used for spatial discretization with flow stabilized via either AUSM+-up or a Roe scheme. The Jacobian-free Newton-Krylov method is used as linear system solver and the lower-upper symmetric Gauss-Seidel method is used for matrix-free preconditioning. In the present formulation, second order approximations of spatial derivatives of the inviscid fluxes are introduced efficiently. Numerical results for Mach 1.93 flow past a sphere, Mach 4 flow past a waverider, and Mach 10.01 flow past a sphere, are presented.

KW - Jacobian-free

KW - solvers

KW - supersonic

KW - viscous flows

KW - hybrid grids

KW - finite element

KW - spatial discretization

KW - Newton-Krylov method

U2 - 10.2514/6.2017-0085

DO - 10.2514/6.2017-0085

M3 - Conference contribution book

AN - SCOPUS:85017280434

T3 - AIAA SciTech Forum

SP - 1

EP - 28

BT - 55th AIAA Aerospace Sciences Meeting

CY - Grapevine, Texas

T2 - 55th AIAA Aerospace Sciences Meeting

Y2 - 9 January 2017 through 13 January 2017

ER -

Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids

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Keywords

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