三維剪流盒之自適性網格與顯示卡加速之實現

Abstract

在此篇論文中，我們描述在GAMER(GPU-accelerated Adaptive Mesh Refinement) 程式中演算“剪流盒近似磁流體方程”以探討吸積盤動力機制的方法。相較於中央處理單元(CPU)，中央處理單元混合圖形運算單元(GPU) 能提升運算效能達十倍。最重要的，當探討問題所需的解析度不斷提高時，利用自適應網格，能有效的降低計算的負擔，進而能更有效率的進行研究。

In this thesis, we describe the implementation of the shearing box approximation with the GAMER (GPU-Accelerated Adaptive MEsh Refinement ) MHD (Magnetohydrodynamics) code for studies of accretion disks . The CPU (Central Process Units)-GPU (Graphic Process Units) hybrid computation, a major feature of GAMER, can ideally make performances more than ten times faster than CPUs-based computation. Since MRI (Magnetorotational Instability) in the weakly magnetize disk is highly dependent on the resolution of simulations, the key feature we introduce here is the realization of the AMR (Adaptive Mesh Refinement) scheme in a shearing box. The AMR scheme can efficiently enhance the resolution on crucial structures in small regions while not to increase the computation cost. Two techniques introduced in the Athena code (James M. Stone, 2010), the Crank-Nicholson update for the energy conservation of pure HYDRO cases and the orbital advection (FARGO) for more efficient and accurate calculation, are also implemented in my code. Difficulties and resolution of implementing the above two techniques to fit the AMR scheme and GPU structure will be discussed in this thesis. Results compared with previous works and performance tests are also presented.