GAMER 是一個利用繪圖處理單元(Graphic-processing-unit, GPU) 加 速及自適網格解析度調整(Adaptive-Mesh-Refinement, AMR) 的天文物理應用模擬程式。此程式已順利擴展成可以數值模擬磁流體動力學 (Magnetohydrodynamics, MHD)。磁流體動力學的數值模擬演算法是 具有限制傳輸(Constraint transport, CT) 技術的逆流邊角傳輸(Cornertransport-upwind, CTU) 演算法。另一方面,散度保持算符(Divergentpreserving operator) 保證了自適網格解析度調整中磁場的零散度條件。模擬結果顯示磁流體GAMER 程式跟其他高解析度均勻網格模擬一樣準確。我們引進一個新的三維測試問題。在此問題中磁場滿足阿諾德-貝爾特拉米-柴爾德里斯(Arnold-Beltrami-Childress) 樣態。這樣的電漿組態一開始會變成有片狀電流密度的紊流,但最後將收斂到最低能量的平衡態。此測試問題很適合檢驗本程式的效能。本程式在單一K20X 的繪圖處理單元下每秒可以演化2×10^7個網格,比藍水(Blue Waters) 超級電腦上的一顆擁有16個核心的中央處理單元(Center-processing-unit, CPU) 快25倍。我們同時發現當使用1024 個藍水超級電腦的計算節點,此程式的平行效率可高達70個百分點。 我們分析在輻射主宰時期的波形態暗物質,或者稱作 ψ 暗物質之線性微擾。在此分析中,暗物質微擾的演化可分成四個階段。其中在質量震盪(Mass oscillation) 之後的晚期階段,長波的 ψ 暗物質微擾幾乎和冷暗物質(Cold dark matter, CDM) 模型雷同。然而對於中短波的情況,在整個演化過程中,沒有一個階段跟冷暗物質一樣。我們同時討論餘弦型態純量場勢能的軸子模型(Axion model)。軸子模型的演化幾乎與 ψ 暗物質相同。但當軸子初始角度非常靠近勢能的頂端,有三個新特徵會顯現。其中最新穎的特徵是在某些波數的範圍內,頻譜會比冷暗物質高。這樣的差異可能會非常大以致於造成紅移10 以上的高紅移宇宙有顯著的改變。亞視界(Sub-horizon) 的擾動可以被馬蒂厄(Mathieu) 方程式準確地描述且受到參數不穩定(Parametric instability)的影響。這解釋了此新穎的特徵。
GAMER, a Graphic-processing-unit-accelerated Adaptive-MEsh-Refinement Astrophysical code, is extended to support magnetohydrodynamics (MHD), where the solver features the corner-transport-upwind (CTU) scheme with the constraint transport (CT) technique. The divergent preserving operator for adaptive mesh refinement (AMR) is applied to reinforce the divergence-free constraint on the magnetic field. Numerical results show GAMER-MHD is as robust as those given by high-resolution uniform-grid runs. We explore a new 3D MHD test, where the magnetic field assumes the Arnold-Beltrami- Childress (ABC) configuration, temporarily becomes turbulent with current sheets and finally settles to a lowest-energy equilibrium state. This 3D problem is adopted for the performance test of GAMER-MHD. The single-GPU performance can reach 2×10^7 cell-updates/sec for K20X and is 25 times faster than a single 16-core CPU on the Blue Waters supercomputer. We also demonstrate a parallel efficiency of 70% using 1024 nodes on Blue Waters. Linear perturbations of the wave dark matter, or ψ dark matter ( ψ DM), in the radiation-dominant era are analyzed. We identify four phases of evolution for ψ DM perturbations. While in late stages after mass oscillation long-wave ψ DM perturbations are almost identical to cold dark matter (CDM) perturbations except that intermediate-to-short waves that bear no resemblance with those of CDM throughout the whole evolutionary history. We also discuss the axion model with a cosine field potential. The evolution of axion models are almost identical to those of ψ DM, but three new features are found in the extreme case where the initial axion angle is near the field potential top. A particularly novel new feature is the spectral excess relative to the CDM model in some wave number range, where the excess may be so large that landscapes of high-redshift universe beyond z = 10 can be significantly altered. The sub-horizon perturbations are accurately described by Mathieu's equation and subjected to parametric instability, which explains this novel feature.
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