| Summary: | 碩士 === 國立臺灣大學 === 天文物理研究所 === 105 === 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.
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