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Title: A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids

Abstract

Here this work focuses on the development of a high-performance fourth-order finite-volume method to solve the nonlinear partial differential equations governing the compressible Navier–Stokes equations on a Cartesian grid with adaptive mesh refinement. The novelty of the present study is to introduce the loop chaining concept to this complex fourth-order fluid dynamics algorithm for significant improvement in code performance on parallel machines. Specific operations involved in the algorithm include the finite-volume formulation of fourth-order spatial discretization stencils and optimal inter-loop parallelization strategies. Numerical fluxes of the Navier–Stokes equations comprise the hyperbolic (inviscid) and elliptic (viscous) ​components. The hyperbolic flux is evaluated using high-resolution Godunov’s method and the elliptic flux is based on fourth-order centered-difference methods everywhere in the computational domain. The use of centered-difference methods everywhere supports the idea of fusing modular codes to achieve high efficiency on modern computers. Temporal discretization is performed using the standard fourth-order ​Runge–Kutta method. The fourth-order accuracy of solution in space and time is verified with a transient Couette flow problem. The algorithm is applied to solve the Sod’s shock tube and the transient flat-plate boundary layer flow. The numerical predictions are validated by comparing to the analytical solutions. The performance of the baselinemore » code is compared to that of the fused scheme which fuses modular codes via loop chaining concept and a significant improvement in execution time is observed.« less

Authors:
; ;
Publication Date:
Research Org.:
Colorado State Univ., Fort Collins, CO (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); National Science Foundation (NSF)
OSTI Identifier:
1991654
Alternate Identifier(s):
OSTI ID: 1406930; OSTI ID: 1533588
Grant/Contract Number:  
EE0006086; B604249; CCF-1422725
Resource Type:
Published Article
Journal Name:
Computers and Mathematics with Applications (Oxford)
Additional Journal Information:
Journal Name: Computers and Mathematics with Applications (Oxford) Journal Volume: 72 Journal Issue: 9; Journal ID: ISSN 0898-1221
Publisher:
Elsevier
Country of Publication:
United Kingdom
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; high-order partial differential equations algorithm; high-performance computational fluid dynamics algorithm; fourth-order finite-volume method; programming model; loop chaining; parallel adaptive mesh refinement

Citation Formats

Guzik, S. M., Gao, X., and Olschanowsky, C. A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids. United Kingdom: N. p., 2016. Web. doi:10.1016/j.camwa.2016.08.004.
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Guzik, S. M., Gao, X., & Olschanowsky, C. A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids. United Kingdom. https://doi.org/10.1016/j.camwa.2016.08.004
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Guzik, S. M., Gao, X., and Olschanowsky, C. Tue . "A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids". United Kingdom. https://doi.org/10.1016/j.camwa.2016.08.004.
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@article{osti_1991654,
title = {A high-performance finite-volume algorithm for solving partial differential equations governing compressible viscous flows on structured grids},
author = {Guzik, S. M. and Gao, X. and Olschanowsky, C.},
abstractNote = {Here this work focuses on the development of a high-performance fourth-order finite-volume method to solve the nonlinear partial differential equations governing the compressible Navier–Stokes equations on a Cartesian grid with adaptive mesh refinement. The novelty of the present study is to introduce the loop chaining concept to this complex fourth-order fluid dynamics algorithm for significant improvement in code performance on parallel machines. Specific operations involved in the algorithm include the finite-volume formulation of fourth-order spatial discretization stencils and optimal inter-loop parallelization strategies. Numerical fluxes of the Navier–Stokes equations comprise the hyperbolic (inviscid) and elliptic (viscous) ​components. The hyperbolic flux is evaluated using high-resolution Godunov’s method and the elliptic flux is based on fourth-order centered-difference methods everywhere in the computational domain. The use of centered-difference methods everywhere supports the idea of fusing modular codes to achieve high efficiency on modern computers. Temporal discretization is performed using the standard fourth-order ​Runge–Kutta method. The fourth-order accuracy of solution in space and time is verified with a transient Couette flow problem. The algorithm is applied to solve the Sod’s shock tube and the transient flat-plate boundary layer flow. The numerical predictions are validated by comparing to the analytical solutions. The performance of the baseline code is compared to that of the fused scheme which fuses modular codes via loop chaining concept and a significant improvement in execution time is observed.},
doi = {10.1016/j.camwa.2016.08.004},
journal = {Computers and Mathematics with Applications (Oxford)},
number = 9,
volume = 72,
place = {United Kingdom},
year = {Tue Nov 01 00:00:00 EDT 2016},
month = {Tue Nov 01 00:00:00 EDT 2016}
}
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https://doi.org/10.1016/j.camwa.2016.08.004
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Works referenced in this record:

A Fourth-Order Scheme for the Compressible Navier-Stokes Equations
conference, January 2015

Local adaptive mesh refinement for shock hydrodynamics
journal, May 1989

On the Impulsive Motion of a flat Plate in a Viscous Fluid
journal, January 1951

  • Stewartson, K.
  • The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 4, Issue 2
  • DOI: 10.1093/qjmam/4.2.182

Loop Chaining: A Programming Abstraction for Balancing Locality and Parallelism
conference, May 2013

  • Krieger, Christopher D.; Strout, Michelle Mills; Olschanowsky, Catherine
  • 2013 IEEE International Symposium on Parallel & Distributed Processing, Workshops and Phd Forum
  • DOI: 10.1109/IPDPSW.2013.68

A high-order finite-volume method for conservation laws on locally refined grids
journal, January 2011

  • McCorquodale, Peter; Colella, Phillip
  • Communications in Applied Mathematics and Computational Science, Vol. 6, Issue 1
  • DOI: 10.2140/camcos.2011.6.1

Unsteady viscous flows and Stokes's first problem
journal, May 2010

A freestream-preserving fourth-order finite-volume method in mapped coordinates with adaptive-mesh refinement
journal, December 2015

A parallel adaptive numerical method with generalized curvilinear coordinate transformation for compressible Navier-Stokes equations: PARALLEL ADAPTIVE NUMERICAL METHODS ON MAPPED GRIDS
journal, April 2016

  • Gao, X.; Owen, L. D.; Guzik, S. M. J.
  • International Journal for Numerical Methods in Fluids, Vol. 82, Issue 10
  • DOI: 10.1002/fld.4235

A Study on Balancing Parallelism, Data Locality, and Recomputation in Existing PDE Solvers
conference, November 2014

  • Olschanowsky, Catherine; Strout, Michelle Mills; Guzik, Stephen
  • SC14: International Conference for High Performance Computing, Networking, Storage and Analysis
  • DOI: 10.1109/SC.2014.70

Numerical simulation of laminar reacting flows with complex chemistry
journal, December 2000

A Fourth-Order Viscous Operator on Mapped Grids
conference, January 2016

  • Owen, Landon D.; Guzik, Stephen M.; Gao, Xinfeng
  • 54th AIAA Aerospace Sciences Meeting
  • DOI: 10.2514/6.2016-0604

A survey of several finite difference methods for systems of nonlinear hyperbolic conservation laws
journal, April 1978

A parallel solution-adaptive scheme for ideal magnetohydrodynamics
conference, February 2013

  • Groth, C.; De Zeeuw, D.; Powell, K.
  • 14th Computational Fluid Dynamics Conference
  • DOI: 10.2514/6.1999-3273

A fourth-order boundary treatment for viscous fluxes on Cartesian grid finite-volume methods
conference, January 2014

  • Gao, Xinfeng; Guzik, Stephen; Colella, Phillip
  • 52nd Aerospace Sciences Meeting
  • DOI: 10.2514/6.2014-1277

A High-Order Finite-Volume Method for Combustion
conference, January 2016

  • Gao, Xinfeng; Owen, Landon D.; Guzik, Stephen M.
  • 54th AIAA Aerospace Sciences Meeting
  • DOI: 10.2514/6.2016-1808

Roofline: an insightful visual performance model for multicore architectures
journal, April 2009

  • Williams, Samuel; Waterman, Andrew; Patterson, David
  • Communications of the ACM, Vol. 52, Issue 4
  • DOI: 10.1145/1498765.1498785

Petascale Block-Structured AMR Applications without Distributed Meta-data
book, January 2011

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