Application of unstructured and adaptive mesh Finite Volume Methods applied to GPU parallel computing

論文翻譯標題: 運用非結構性及適應性網格的有限體積法應用在圖形顯示晶片的平行計算
  • 張 介明

學生論文: Master's Thesis


Conventional transient Computational Fluid Dynamics is focused on the structured Cartesian Grid Since nowadays our gadgets become smaller and smaller people usually deposit more objects in the same space which makes our computational domain become sophistication In such cases it’s hard to continue applying Structured Cartesian grid because the mesh can’t fit the region well One of this study applies unstructured grid to overcome the three-dimensional complicated geometry problem For the sake of developing our unstructured solver we employ two dimensional unstructured Cartesian grid and then extend into three dimensional unstructured tetrahedral grid However it’s high time-consuming to execute the unstructured solver because of accessing the memory Thus we apply the Graphics Processing Units (GPUs) parallel computing architecture to improve our computational speed The maximum speed-up is approximately 59x compared with Nvidia GTX-Titan Black and Intel i5-4590 CPU core for Analytical Riemann solver Moreover the speed-up is able to increase up to 70x with employing texture memory The other research I have done is applying Adaptive Mesh Refinement (AMR) algorithm on the transient simulation Inside the flow field some regions may be under-resolved making us difficult to capture the characteristic of the flow field or over-resolved causing inefficiency computation During the computing we use a dimensionless variable - local normalized density gradient (?ρ/ρ??x) - to determine the regions are under-refined which will be flagged to split into small cells while the regions are over-refined which will be marked to combine with neighboring cells Although the total flux computing work is decreased a lot by applying AMR technique the AMR performance is still an order less than the structured grid’s performance because the poor GPU memory bandwidth and time required for mesh adaption confine the overall performance Another disadvantage of AMR technique for transient flow simulation may feed back into the physics of the flow field and lead to produce non-physical flow features which may not be presented on structured grid in the same minimum grid density In addition to the application of Analytical Riemann Solver the research also applies HLL (Haerten Lax and Van Leer) method and SHLL (Split HLL) method on tetrahedral grid In spite of HLL and SHLL method decreasing speed-up performance the total computational time reduces dramatically Due to the simplification of flux calculation however the numerical diffusion will appear and influence our final results The TVD-type scheme also be executed on the research to increase the spatial accuracy into second order and the MINMOD limiter is employed to avoid the non-physical oscillations over the space
獎項日期2016 六月 23
監督員Matt-Hew Smith (Supervisor)