使用數值方法解流體形式的薛丁格方程式

Numerically solving the Schrödinger equation in hydrodynamic form

黃冠維(Kuan-Wei Huang)

指導教授 ： 闕志鴻

國立臺灣大學/理學院/物理學研究所/碩士(2016年)

https://doi.org/10.6342/NTU201601646

摘要

ψ 暗物質的動力學可用薛丁格–泊松 (Schrödinger-Poisson) 方程式加
以描述。我們使用 Lax–Wendroff 方法在流體形式下做數值計算。我們
以一些已知的解析解（如：平面波、微擾波、高斯波包、駐波、與漩
渦對）測試程式的準確度。演算法中產生的一些數值問題可以藉由數
值逸散、數學形式的改變、與通量項正規化加以改進。

關鍵字

數值模擬 ； 宇宙學 ； 暗物質 ； 宇宙結構形成

並列摘要

The dynamics of the quantum wave dark matter (ψDM) can be described by the Schrödinger-Poisson equation. We numerically solve it in hydrodynamic form by the Lax–Wendroff method. The accuracy of the program is tested with several analytic solutions, e.g., plane wave, perturbation wave, Gaussian wave packet, standing wave, vortex pairs. We encounter some numerical problems so that we improve the algorithm by adding numerical diffusion, slightly changing the mathematical form, and regularizing the flux term.

並列關鍵字

simulation ； cosmology ； dark matter ； cosmic structure formation

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