Acceleration of a Finite-Difference WENO Scheme for Large-Scale Simulations on Many-Core Architectures

Abstract

Current trends on high performance computing are moving towards the deployment of several cores on the same chip of modern processors in order to achieve substantial execution speedup through the extraction of the potential fine-grain parallelism of applications. At the forefront of this trend we find nowadays the modern Graphics Processors Units (GPUs), which due to their simplistic design are able to encompass hundreds of independent processing units on a single chip in contrast to their respective CPUs, which at the moment include only a few cores on the same chip. In order to study the potential speedup of computationally intensive applications that utilize the many-core architecture of GPUs, this paper presents a highly accelerated implementation of the finitedifference weighted essentially non-oscillatory (WENO) scheme. This method is suitable for direct numerical simulations (DNS) large eddy simulations (LES) of compressible turbulence and requires large computing resources in order to achieve high Reynolds numbers. Our implementation targets on large-scale simulations using the CUDA parallel programming and constitues a paradigm of GPU's applications in CFD. The results of the current implementation demonstrate that such a computationally intensive application could be highly accelerated running on the NVIDIA Tesla C1070 many-core GPU.

The features of the of truncation and approximation errors’ geometry on the ensemble of numerical solutions

“…Проведена серия численных расчетов с использованием алгоритмов разного порядка аппроксимации (от первого до пятого) [23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] для Edney I и Edney VI на сетках 100*100 и 400*400. Ниже представлены данные расчетов для Edney I (100*100).…”

A Sparse Matrix Personality for the Convey HC-1

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Parallelizing a high-order WENO scheme for complicated flow structures on GPU and MIC

“…Since GPUs with the Compute Unified Device Architecture (CUDA) programming model support were first launched by NVIDIA Corporation in 2006, several groups have applied them to reduce the computational time of the WENO schemes for CFD simulations. Athanasios S. Antoniou et al [5] presented a highly accelerated implementation of the finite-difference WENO scheme for large-scale simulations and reported a speedup of 53 on the average for the several mesh sizes compared to sequential execution. Michael Griebel et al [6] implemented the 5th order WENO scheme for a two-phase solver on CUDA-enabled GPUs and observed an impressive speedup of 69.6 on eight GPUs/CPUs in contrast to a single CPU.…”