Solution of the euler and navier stokes equations on parallel processors using a transposed/thomas adi algorithm

Thomas S. Chyczewski; Frank Marconi; Richard B. Pelz; Enrique N. Curchitser

doi:10.2514/6.1993-3310

Solution of the euler and navier stokes equations on parallel processors using a transposed/thomas adi algorithm

Thomas S. Chyczewski, Frank Marconi, Richard B. Pelz, Enrique N. Curchitser

Research output: Contribution to conference › Paper › peer-review

1 Scopus citations

Abstract

The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries. The spatial derivatives are evaluated to second order accuracy with upwind differencing and the equations are solved implicitly using AD1 factorization. The Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme. The recursion inherent in this method is dealt with by transposing the domain amongst the processors so that there is no communication required in order to solve the tridiagonals once the transpose is done. A couple of transpose schemes were considered and results are presented for the most efficient. Very good times are achieved for realistic problems when run on a coarse to medium grain machine. The method is compared with other parallel schemes. The code was developed and run on an nCUBE/2 and also run on a Thinking Machines CM-5 for a performance comparison and to illustrate portability of the code.

Original language	English (US)
Pages	144-154
Number of pages	11
DOIs	https://doi.org/10.2514/6.1993-3310
State	Published - 1993
Event	11th Computational Fluid Dynamics Conference, 1993 - Orlando, United States Duration: Jul 6 1993 → Jul 9 1993

Conference

Conference	11th Computational Fluid Dynamics Conference, 1993
Country/Territory	United States
City	Orlando
Period	7/6/93 → 7/9/93

All Science Journal Classification (ASJC) codes

Mechanical Engineering
Fluid Flow and Transfer Processes

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10.2514/6.1993-3310

Cite this

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title = "Solution of the euler and navier stokes equations on parallel processors using a transposed/thomas adi algorithm",

abstract = "The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries. The spatial derivatives are evaluated to second order accuracy with upwind differencing and the equations are solved implicitly using AD1 factorization. The Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme. The recursion inherent in this method is dealt with by transposing the domain amongst the processors so that there is no communication required in order to solve the tridiagonals once the transpose is done. A couple of transpose schemes were considered and results are presented for the most efficient. Very good times are achieved for realistic problems when run on a coarse to medium grain machine. The method is compared with other parallel schemes. The code was developed and run on an nCUBE/2 and also run on a Thinking Machines CM-5 for a performance comparison and to illustrate portability of the code.",

author = "Chyczewski, {Thomas S.} and Frank Marconi and Pelz, {Richard B.} and Curchitser, {Enrique N.}",

note = "Publisher Copyright: {\textcopyright} 1993 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.; 11th Computational Fluid Dynamics Conference, 1993 ; Conference date: 06-07-1993 Through 09-07-1993",

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doi = "10.2514/6.1993-3310",

language = "English (US)",

pages = "144--154",

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AU - Chyczewski, Thomas S.

AU - Marconi, Frank

AU - Pelz, Richard B.

AU - Curchitser, Enrique N.

PY - 1993

Y1 - 1993

N2 - The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries. The spatial derivatives are evaluated to second order accuracy with upwind differencing and the equations are solved implicitly using AD1 factorization. The Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme. The recursion inherent in this method is dealt with by transposing the domain amongst the processors so that there is no communication required in order to solve the tridiagonals once the transpose is done. A couple of transpose schemes were considered and results are presented for the most efficient. Very good times are achieved for realistic problems when run on a coarse to medium grain machine. The method is compared with other parallel schemes. The code was developed and run on an nCUBE/2 and also run on a Thinking Machines CM-5 for a performance comparison and to illustrate portability of the code.

AB - The Euler and Navier Stokes equations are discretized and numerically solved on distributed memory parallel processors for airfoil geometries. The spatial derivatives are evaluated to second order accuracy with upwind differencing and the equations are solved implicitly using AD1 factorization. The Thomas Algorithm is used to solve the block tridiagonal matrices that result from the implicit AD1 scheme. The recursion inherent in this method is dealt with by transposing the domain amongst the processors so that there is no communication required in order to solve the tridiagonals once the transpose is done. A couple of transpose schemes were considered and results are presented for the most efficient. Very good times are achieved for realistic problems when run on a coarse to medium grain machine. The method is compared with other parallel schemes. The code was developed and run on an nCUBE/2 and also run on a Thinking Machines CM-5 for a performance comparison and to illustrate portability of the code.

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Solution of the euler and navier stokes equations on parallel processors using a transposed/thomas adi algorithm

Abstract

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