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Title: Scalability of preconditioners as a strategy for parallel computation of compressible fluid flow

Abstract

Parallel implementations of a Newton-Krylov-Schwarz algorithm are used to solve a model problem representing low Mach number compressible fluid flow over a backward-facing step. The Mach number is specifically selected to result in a numerically {open_quote}stiff{close_quotes} matrix problem, based on an implicit finite volume discretization of the compressible 2D Navier-Stokes/energy equations using primitive variables. Newton`s method is used to linearize the discrete system, and a preconditioned Krylov projection technique is used to solve the resulting linear system. Domain decomposition enables the development of a global preconditioner via the parallel construction of contributions derived from subdomains. Formation of the global preconditioner is based upon additive and multiplicative Schwarz algorithms, with and without subdomain overlap. The degree of parallelism of this technique is further enhanced with the use of a matrix-free approximation for the Jacobian used in the Krylov technique (in this case, GMRES(k)). Of paramount interest to this study is the implementation and optimization of these techniques on parallel shared-memory hardware, namely the Cray C90 and SGI Challenge architectures. These architectures were chosen as representative and commonly available to researchers interested in the solution of problems of this type. The Newton-Krylov-Schwarz solution technique is increasingly being investigated for computational fluid dynamicsmore » (CFD) applications due to the advantages of full coupling of all variables and equations, rapid non-linear convergence, and moderate memory requirements. A parallel version of this method that scales effectively on the above architectures would be extremely attractive to practitioners, resulting in efficient, cost-effective, parallel solutions exhibiting the benefits of the solution technique.« less

Authors:
Publication Date:
Research Org.:
Idaho National Lab. (INL), Idaho Falls, ID (United States)
Sponsoring Org.:
USDOE, Washington, DC (United States)
OSTI Identifier:
237435
Report Number(s):
INEL-96/125
ON: DE96010357; TRN: 96:003273
DOE Contract Number:  
AC07-94ID13223
Resource Type:
Technical Report
Resource Relation:
Other Information: PBD: May 1996
Country of Publication:
United States
Language:
English
Subject:
42 ENGINEERING NOT INCLUDED IN OTHER CATEGORIES; 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPRESSIBLE FLOW; PARALLEL PROCESSING; NAVIER-STOKES EQUATIONS; NEWTON METHOD; SCALING LAWS; ALGORITHMS; CRAY COMPUTERS

Citation Formats

Hansen, G A. Scalability of preconditioners as a strategy for parallel computation of compressible fluid flow. United States: N. p., 1996. Web. doi:10.2172/237435.
Hansen, G A. Scalability of preconditioners as a strategy for parallel computation of compressible fluid flow. United States. https://doi.org/10.2172/237435
Hansen, G A. 1996. "Scalability of preconditioners as a strategy for parallel computation of compressible fluid flow". United States. https://doi.org/10.2172/237435. https://www.osti.gov/servlets/purl/237435.
@article{osti_237435,
title = {Scalability of preconditioners as a strategy for parallel computation of compressible fluid flow},
author = {Hansen, G A},
abstractNote = {Parallel implementations of a Newton-Krylov-Schwarz algorithm are used to solve a model problem representing low Mach number compressible fluid flow over a backward-facing step. The Mach number is specifically selected to result in a numerically {open_quote}stiff{close_quotes} matrix problem, based on an implicit finite volume discretization of the compressible 2D Navier-Stokes/energy equations using primitive variables. Newton`s method is used to linearize the discrete system, and a preconditioned Krylov projection technique is used to solve the resulting linear system. Domain decomposition enables the development of a global preconditioner via the parallel construction of contributions derived from subdomains. Formation of the global preconditioner is based upon additive and multiplicative Schwarz algorithms, with and without subdomain overlap. The degree of parallelism of this technique is further enhanced with the use of a matrix-free approximation for the Jacobian used in the Krylov technique (in this case, GMRES(k)). Of paramount interest to this study is the implementation and optimization of these techniques on parallel shared-memory hardware, namely the Cray C90 and SGI Challenge architectures. These architectures were chosen as representative and commonly available to researchers interested in the solution of problems of this type. The Newton-Krylov-Schwarz solution technique is increasingly being investigated for computational fluid dynamics (CFD) applications due to the advantages of full coupling of all variables and equations, rapid non-linear convergence, and moderate memory requirements. A parallel version of this method that scales effectively on the above architectures would be extremely attractive to practitioners, resulting in efficient, cost-effective, parallel solutions exhibiting the benefits of the solution technique.},
doi = {10.2172/237435},
url = {https://www.osti.gov/biblio/237435}, journal = {},
number = ,
volume = ,
place = {United States},
year = {1996},
month = {5}
}