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Development of a Parallel Explicit Finite-Volume Euler Equation Solver using the Immersed Boundary Method with Hybrid MPI-CUDA Paradigm

Published online by Cambridge University Press:  11 October 2019

F. A. Kuo ,
C. H. Chiang ,
M. C. Lo  and
J. S. Wu Open the ORCID record for J. S. Wu [Opens in a new window]
F. A. Kuo
Affiliation:
Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchu, Taiwan National Center for High-Performance ComputingNational Applied Research LaboratoriesHsinchu, Taiwan
C. H. Chiang
Affiliation:
Department of Mechanical and Automation EngineeringI-Shou UniversityKaohsiung, Taiwan
M. C. Lo
Affiliation:
Department of Mechanical and Aerospace EngineeringChung Cheng Institute of Technology, National Defense UniversityTaoyuan, Taiwan
J. S. Wu*
Affiliation:
Department of Mechanical EngineeringNational Chiao Tung UniversityHsinchu, Taiwan
*
*Corresponding author (chongsin@faculty.nctu.edu.tw)
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Abstract

This study proposed the application of a novel immersed boundary method (IBM) for the treatment of irregular geometries using Cartesian computational grids for high speed compressible gas flows modelled using the unsteady Euler equations. Furthermore, the method is accelerated through the use of multiple Graphics Processing Units – specifically using Nvidia’s CUDA together with MPI - due to the computationally intensive nature associated with the numerical solution to multi-dimensional continuity equations. Due to the high degree of locality required for efficient multiple GPU computation, the Split Harten-Lax-van-Leer (SHLL) scheme is employed for vector splitting of fluxes across cell interfaces. NVIDIA visual profiler shows that our proposed method having a computational speed of 98.6 GFLOPS and 61% efficiency based on the Roofline analysis that provides the theoretical computing speed of reaching 160 GLOPS with an average 2.225 operations/byte. To demonstrate the validity of the method, results from several benchmark problems covering both subsonic and supersonic flow regimes are presented. Performance testing using 96 GPU devices demonstrates a speed up of 89 times that of a single GPU (i.e. 92% efficiency) for a benchmark problem employing 48 million cells. Discussions regarding communication overhead and parallel efficiency for varying problem sizes are also presented.

Keywords

Euler equationsFinite volume methodImmersed boundary methodGPU
Type
Research Article
Information
Journal of Mechanics , Volume 36 , Issue 1 , February 2020 , pp. 87 - 102
Copyright
Copyright © 2019 The Society of Theoretical and Applied Mechanics 

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