非靜水淺水流的雙曲線模型的數值研究

A numerical study of hyperbolic models for non-hydrostatic shallow water flow

洪彥仲(Yen-Chung Hung)

指導教授 ： 薛克民

國立臺灣大學/理學院/應用數學科學研究所/碩士(2021年)

https://doi.org/10.6342/NTU202101519

摘要

在這篇論文中，我們對於非靜水色散模型如BBM模型及SGN模型做了解析及數值的研究。我們推導了週期性行波解及Whitham方程作為數值方法的驗證。此外，我們在數值結果上比較了原始模型及他們各自的雙曲線模型。兩個雙曲線模型都與原始模型在數值結果上相當吻合。而後，我們討論了在計算包含水底地形的SGN模型時，數值方法的處理。我們模仿了[17]、[1]和[27]中描述的方法，並提出了一種保持靜止狀態和穩態解的數值方法。

關鍵字

Benjamin-Bona-Mahony方程 ； Serre-Green-Naghdi方程 ； 色散震波 ； 平衡態結構 ； 地形學 ； 乾燥態 ； Saint-Venant方程

並列摘要

In this thesis, we do analytic and numerical studies on non-hydrostatic dispersive models, BBM model and SGN model. Derivation of periodic travelling wave and Whitham equation for numerical validation are done. We also compare the original model and their hyperbolic model in the numerical sense. Both hyperbolic models agree with the original models well. Moreover, we discuss the artificial numerical treatment when bottom terms is included. We mimic the method described in [17], [1], and [27] and propose a numerical scheme preserving the motionless state and steady-state solution.

並列關鍵字

Benjamin-Bona-Mahony equation ； Serre-Green-Naghdi equation ； dispersive shock wave ； well-balanced scheme ； topography ； dry state ； Saint-Venant equation

參考文獻

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