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Time integration algorithms for the two-dimensional Euler equations on unstructured meshesExplicit and implicit time integration algorithms for the two-dimensional Euler equations on unstructured grids are presented. Both cell-centered and cell-vertex finite volume upwind schemes utilizing Roe's approximate Riemann solver are developed. For the cell-vertex scheme, a four-stage Runge-Kutta time integration, a fourstage Runge-Kutta time integration with implicit residual averaging, a point Jacobi method, a symmetric point Gauss-Seidel method and two methods utilizing preconditioned sparse matrix solvers are presented. For the cell-centered scheme, a Runge-Kutta scheme, an implicit tridiagonal relaxation scheme modeled after line Gauss-Seidel, a fully implicit lower-upper (LU) decomposition, and a hybrid scheme utilizing both Runge-Kutta and LU methods are presented. A reverse Cuthill-McKee renumbering scheme is employed for the direct solver to decrease CPU time by reducing the fill of the Jacobian matrix. A comparison of the various time integration schemes is made for both first-order and higher order accurate solutions using several mesh sizes, higher order accuracy is achieved by using multidimensional monotone linear reconstruction procedures. The results obtained for a transonic flow over a circular arc suggest that the preconditioned sparse matrix solvers perform better than the other methods as the number of elements in the mesh increases.
Document ID
19950056486
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
Authors
Slack, David C.
(AeroSoft, Inc. Blacksburg, VA, United States)
Whitaker, D. L.
(Analytical Services and Materials, Inc. Hampton, VA, United States)
Walters, Robert W.
(Virginia Polytechnic Institute and State University Blacksburg, VA, United States)
Date Acquired
August 16, 2013
Publication Date
June 1, 1994
Publication Information
Publication: AIAA Journal
Volume: 32
Issue: 6
ISSN: 0001-1452
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
95A88085
Funding Number(s)
CONTRACT_GRANT: NAG1-776
CONTRACT_GRANT: NAS1-18599
CONTRACT_GRANT: NAG1-992
Distribution Limits
Public
Copyright
Other

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