Computational Fluid Dynamics Computations Using a Preconditioned Krylov Solver on Graphical Processing Units

Abstract

Graphical processing unit (GPU) computation in recent years has seen extensive growth due to advancement in both hardware and software stack. This has led to increase in the use of GPUs as accelerators across a broad spectrum of applications. This work deals with the use of general purpose GPUs for performing computational fluid dynamics (CFD) computations. The paper discusses strategies and findings on porting a large multifunctional CFD code to the GPU architecture. Within this framework, the most compute intensive segment of the software, the BiCGStab linear solver using additive Schwarz block preconditioners with point Jacobi iterative smoothing is optimized for the GPU platform using various techniques in CUDA Fortran. Representative turbulent channel and pipe flow are investigated for validation and benchmarking purposes. Both single and double precision calculations are highlighted. For a modest single block grid of 64 × 64 × 64, the turbulent channel flow computations showed a speedup of about eightfold in double precision and more than 13-fold for single precision on the NVIDIA Tesla GPU over a serial run on an Intel central processing unit (CPU). For the pipe flow consisting of 1.78 × 106 grid cells distributed over 36 mesh blocks, the gains were more modest at 4.5 and 6.5 for double and single precision, respectively.

Machine-Learned Preconditioners for Linear Solvers in Geophysical Fluid Flows

“…All in all, results are similar to [3,28,29,30,2,31,32,4] in that the preconditioning step is very robust against reducing precision and seems to be the part of the elliptic solver where performance gains can be expected while many of the other parts can be quite sensitive to reducing precision. It is an important finding that this general structure can also be found in our specific problem from geophysical fluid dynamics, using a conjugated residual solver with a preconditioner based on tridiagonal inversion, a key component in 3D atmospheric semi-implicit grid-point models.…”

“…To efficiently solve an elliptic problem posed in a thin spherical shell (such as the global atmosphere) ultimately requires matrix inversion-if not in the main solver than at least in its preconditioner. While there is the common opinion that high precision is required for this purpose, there are theoretical studies [2,3,28,29,30] suggesting that mixed-precision approaches could be exploited, and there are already some applications of mixed-precision elliptic solvers in CFD [31,32,4] and also in W&C [13]. Although these approaches may differ in choice of algorithms and applications, a common theme emerges that the preconditioning step may be a good choice for reducing precision, where some work goes as low as half precision arithmetic (16 bits per variable) representing each real number with only 16 bits (as a floating point number) and decimal precision reduced to three digits.…”

Recycling Krylov subspaces for CFD applications and a new hybrid recycling solver

“…GenIDLEST uses domain decomposition-based preconditoners that have been optimized for parallel [26] execution on CPUs and, more recently, on GPUs [27,24]. Optimizations for serial implementations have also been done [28], but here we focus on preconditioners that run fast in parallel.…”

“…The GenIDLEST code spans over 300,000 lines and more than 600 subroutines, and it has modules for the Arbitrary Lagrangian-Eulerian (ALE) Method [19], the Discrete Element Method (DEM) [20], the Immersed Boundary Method (IBM) [21], and for Fluid Structure Interaction (FSI) [22]. The computational algorithms are optimized to take maximum advantage of state-of-the-art hierarchical memory and parallel architectures, with a focus on Message Passing Interface (MPI) and OpenMP-based codes for central processing units (CPUs) [23] and more recently for GPUs [24].…”

High Reynold Number LES of a Rotating Two-Pass Ribbed Duct

“…The comprehensive integrated flow and heat transfer data that can be obtained by LES is unparalleled by current day experimental techniques. The main drawback of high computational cost can be overcome by using modern computing architectures equipped with accelerators such as Graphics Processing Units (GPUs) [111].…”