A gpu-accelerated method for solving the Euler equation by the discontinuous Galerkin method

Abstract

The invention belongs to the fields of computational fluid dynamics and high-performance computing, and relates to a GPU parallel acceleration technology of the discontinuous Galerkin method (DGM), specifically a GPU acceleration method for solving the Euler equation by the discontinuous Galerkin method. The invention adopts tetrahedron grid to divide the solution area, based on basis function, Gaussian integral and numerical flux, GPU is the main computing hardware, and CUDA is the programming model to establish the GPU parallel framework of intermittent Galerkin method. Through the CUDA parallel framework, the management of GPU multithreading is realized, and the efficient memory access is realized through the designed data structure and thread access method. When solving the problem that data exchange between units is not independent in area integration, the method of processing two units according to the parallel surface grid and the calculation thread of each area grid is adopted, which not only avoids the problem that the units are not independent, but also realizes It achieves large-scale parallelism and reduces the amount of computation.

Description

technical field [0001] The invention belongs to the fields of computational fluid dynamics and high-performance computing, and relates to a GPU parallel acceleration technology of the discontinuous Galerkin method (DGM), specifically a GPU acceleration method for solving the Euler equation by the discontinuous Galerkin method. Background technique [0002] The Euler equation is a system of equations describing inviscid fluid in fluid mechanics, and its form is as follows: [0003] u t +▽ F=0 (1) [0004] where U represents the conserved quantity, U t represents the partial derivative of the conserved quantity with respect to time t, F represents the conserved flux, ▽·F represents the divergence of the conserved flux, and in the three-dimensional case, we have [0005] [0006] Among them, ρ is the gas density, u, v, and w are the three velocity components of the gas, e is the total energy per unit volume of the complete gas, and p is the gas pressure. [0007] For the...

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Problems solved by technology

[0018] In view of the above-mentioned problems or deficiencies, in order to solve the problem that the numerical solution of the existing Euler equation DGM combined with the method of multi-core CPU is relatively expensive and relatively inefficient, the present invention provides a discontinuous Galerkin method for solving the Euler equation Based on the characteristics of the discontinuous Galerkin method and the advantages of GPU parallel computing, GPU parallel computing is applied to the discontinuous Galerkin method to solve the Euler equation, which can maximize the advantages of the discontinuous Galerkin method and accelerate Computational Fluid Dynamics Computation in High Precision Format

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