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 proceedingConference contribution book

1 Citation (Scopus)

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.
LanguageEnglish
Title of host publication55th AIAA Aerospace Sciences Meeting
Place of PublicationGrapevine, Texas
Pages1-28
Number of pages28
ISBN (Electronic)9781624104473
DOIs
Publication statusPublished - 5 Jan 2017
Event55th AIAA Aerospace Sciences Meeting - Grapevine, United States
Duration: 9 Jan 201713 Jan 2017
http://scitech.aiaa.org/asm/

Publication series

NameAIAA SciTech Forum
PublisherAmerican Institute of Aeronautics and Astronautics

Conference

Conference55th AIAA Aerospace Sciences Meeting
Abbreviated titleAIAA SciTech 2017
CountryUnited States
CityGrapevine
Period9/01/1713/01/17
Internet address

Fingerprint

Viscous flow
Mach number
Supersonic flow
Newton-Raphson method
Linear systems
Fluxes
Derivatives

Keywords

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

Cite this

Gao, S., Habashi, W. G., Fossati, M., Isola, D., & Baruzzi, G. S. (2017). Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. In 55th AIAA Aerospace Sciences Meeting (pp. 1-28). (AIAA SciTech Forum). Grapevine, Texas. https://doi.org/10.2514/6.2017-0085
Gao, Song ; Habashi, Wagdi G. ; Fossati, Marco ; Isola, Dario ; Baruzzi, Guido S. / Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. 55th AIAA Aerospace Sciences Meeting. Grapevine, Texas, 2017. pp. 1-28 (AIAA SciTech Forum).
@inproceedings{15ac5e339847497fbe97171c08c2ff18,
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.}",
note = "{\circledC}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",
year = "2017",
month = "1",
day = "5",
doi = "10.2514/6.2017-0085",
language = "English",
series = "AIAA SciTech Forum",
publisher = "American Institute of Aeronautics and Astronautics",
pages = "1--28",
booktitle = "55th AIAA Aerospace Sciences Meeting",

}

Gao, S, Habashi, WG, Fossati, M, Isola, D & Baruzzi, GS 2017, Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. in 55th AIAA Aerospace Sciences Meeting. AIAA SciTech Forum, Grapevine, Texas, pp. 1-28, 55th AIAA Aerospace Sciences Meeting, Grapevine, United States, 9/01/17. https://doi.org/10.2514/6.2017-0085

Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. / Gao, Song; Habashi, Wagdi G.; Fossati, Marco; Isola, Dario; Baruzzi, Guido S.

55th AIAA Aerospace Sciences Meeting. Grapevine, Texas, 2017. p. 1-28 (AIAA SciTech Forum).

Research output: Chapter in Book/Report/Conference proceedingConference contribution book

TY - GEN

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

T3 - AIAA SciTech Forum

SP - 1

EP - 28

BT - 55th AIAA Aerospace Sciences Meeting

CY - Grapevine, Texas

ER -

Gao S, Habashi WG, Fossati M, Isola D, Baruzzi GS. Finite-element formulation of a Jacobian-free solver for supersonic viscous flows on hybrid grids. In 55th AIAA Aerospace Sciences Meeting. Grapevine, Texas. 2017. p. 1-28. (AIAA SciTech Forum). https://doi.org/10.2514/6.2017-0085