GPU加速數模於二維不可壓縮穴流之研究

Abstract

圖形處理器(Graphic Processing Unit,GPU) 的開發起初源自於處理電腦遊戲大量貼圖運算，現今透過計算統一架構(Compute Unified Device Architecture,CUDA) 能夠有效的運用其高度計算能力、儲存器帶寬於科學計算方面。在水利方面所面臨的大量計算問題，如集水區淹水演算、三維水理演算及三維動床演算等，數據規模大小已經達到TB甚至於PB量級，因此對計算效能構成了嚴峻的挑戰。本研究藉由GPU以有限差分法求解二維穩態不可壓縮穴流，評估GPU加速於數值模擬之效益。藉由改變穴流長寬比與網格大小，得知網格數量越高，越有平行運算的必要，本研究GPU採用nVidia GeForce GTX 480，CPU方面選用Intel® Core™2 Duo Processor E7400與AMD Athlon II X4 635，在長寬比為7，網格點數達257×1793時，對於intel之CPU有33倍加速效果，AMD之CPU則有44倍加速成效。

The development of Graphic Processing Unit (GPU) originated from processing a great deal of mapping operation in computer games. Nowadays, GPU can apply its strong computing power and bandwidth of storage effectively to science computation by using Compute Unified Device Architecture (CUDA). There are a large amount of calculational problems we will face. For instance, model for watershed inundation, three-dimensional hydraulic model, three-dimensional mobile-bed model etc. The data size above has reached to TB even to PB, and it yields a rigorous challenge to computing efficiency. This study takes GPU combined with finite difference method to solve two-dimensional steady incompressible cavity flow, and evaluates the beneficial result of numerical simulation accelerated. By changing length of cavity flow and size of grid, we find that the more grid number, the more necessary for parallel processing. This study takes nVidia GeForce GTX 480 in GPU, and Intel® Core™2 Duo Processor E7400 and AMD Athlon II X4 635 in CPU. When the aspect ratio is 7 and grid number reaches to 257×1793, there are 33 times acceleration effect in Intel’s CPU and 44 times acceleration effect in AMD’s CPU.