A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics
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PINT 2019
A space-time parallel algorithm with adaptive mesh refinement for computational fluid dynamics Joshua Christopher1 · Robert D. Falgout2 · Jacob B. Schroder3 · Stephen M. Guzik1 · Xinfeng Gao1 Received: 7 December 2019 / Accepted: 31 July 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract This paper describes a space-time parallel algorithm with space-time adaptive mesh refinement (AMR). AMR with subcycling is added to multigrid reduction-in-time (MGRIT) in order to provide solution efficient adaptive grids with a reduction in work performed on coarser grids. This algorithm is achieved by integrating two software libraries: XBraid (Parallel time integration with multigrid. https://computation.llnl.gov/projects/parallel-timeintegration-multigrid) and Chombo (Chombo software package for AMR applications—design document, 2014). The former is a parallel time integration library using multigrid and the latter is a massively parallel structured AMR library. Employing this adaptive space-time parallel algorithm is Chord (Comput Fluids 123:202–217, 2015), a computational fluid dynamics (CFD) application code for solving compressible fluid dynamics problems. For the same solution accuracy, speedups are demonstrated from the use of space-time parallelization over the time-sequential integration on Couette flow and Stokes’ second problem. On a transient Couette flow case, at least a 1.5× speedup is achieved, and with a time periodic problem, a speedup of up to 13.7× over the time-sequential case is obtained. In both cases, the speedup is achieved by adding processors and exploring additional parallelization in time. The numerical experiments show the algorithm is promising for CFD applications that can take advantage of the time parallelism. Future work will focus on improving the parallel performance and providing more tests with complex fluid dynamics to demonstrate the full potential of the algorithm. Keywords Time-parallel · Mesh parallel-in-time · Adaptivity · Multigrid · MGRIT · High-order CFD · Finite-volume
1 Introduction
Communicated by Robert Speck. This work was performed under the auspices of the U.S. Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344 (LLNL-JRNL-798697).
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Joshua Christopher [email protected] Robert D. Falgout [email protected] Jacob B. Schroder [email protected]
1
CFD & Propulsion Laboratory, Colorado State University, Fort Collins, USA
2
Center for Applied Scientific Computing, Lawrence Livermore National Laboratory, Livermore, USA
3
Department of Mathematics and Statistics, University of New Mexico, Albuquerque, USA
Fluid flows encountered in the chemical propulsion systems in aerospace engineering are often highly turbulent and combusting. Accurately predicting the interactions among multiple physical phenomena, such as thermodynamics, turbulence, chemical reactions, and scalar transport, over a wide range of spatial and temporal scales, is difficult but necessary for engineering design. This r
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