Using Generalized Finite Difference Method for Three-Dimensional Parallel-Computation Numerical Wave Flume Based on Viscous Incompressible Fluid

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Project title

Code/計畫編號

MOST107-2221-E019-011

Translated Name/計畫中文名

以廣義有限差分法建立黏性不可壓縮流體為基礎之三維平行化數值波浪水槽

Project Coordinator/計畫主持人

Chia-Ming Fan

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Harbor and River Engineering

Website

https://www.grb.gov.tw/search/planDetail?id=12670623

Year

2018

Start date/計畫起

01-08-2018

Expected Completion/計畫迄

31-07-2019

Bugetid/研究經費

628千元

ResearchField/研究領域

土木水利工程

本計畫目標為以廣義有限差分法為主要數值離散方法，開發一套模擬黏性不可壓縮流體之三維平行化數值波浪水槽，以快速電腦模擬的方式研究波浪傳遞時之非線性動態變化現象，可提供給學術研究、工程設計與科普教育使用。本計畫之內容為過去兩年科技部計畫之延伸研究，將波浪水槽中之研究流體由勢能流體改為黏性不可壓縮流體，以擴大數值波浪水槽之適用範圍，雖然會大幅增加開發電腦模式之困難度，但研究完成後能用以模擬真實流體動態運動行為。廣義有限差分法是新開發的無網格法之一，能避免建立網格與數值積分等耗時的工作，可增加電腦模擬之演算效率，且沒有一般無網格法會產生的病態矩陣與自由參數等問題，具有非常良好的準確性、穩定性與計算效率，特別適合有自由水面變化之數值波浪水槽開發。黏性不可壓縮流體之數學描述為那維爾-史托克斯方程式，本計畫以任意拉格朗日歐拉法改寫此控制方程式，可以準確加入計算點位移動速度，而後採用廣義有限差分法與運算子拆解法進行方程式的空間與時間離散。任意拉格朗日歐拉法兼具拉格朗日法與歐拉法之優點，可以同時考慮撰寫電腦模式之簡易性與模擬自由水面位置之準確性，且適合與廣義有限差分法合併進行電腦模擬；運算子拆解法簡化那維爾-史托克斯方程式的計算流程，將一個時間間格內的計算流程簡化為三個步驟，而且只要求解一個卜松方程式之邊界值問題，具有良好的計算效率。另外，在水槽之入口與出口處，本計畫之電腦模擬模式加入不同之造波機以及佈置數值海綿消能層，能有效產生不同形式的入射波浪，也能避免不必要的反射波浪進入模擬水槽中。由於此三維數值波浪水槽是以廣義有限差分法為基礎，廣義有限差分法是新發展的配點型式無網格法，適合於平行化程式撰寫，因此本計劃將加入繪圖卡平行計算程式撰寫方式，以增加三維數值波浪水槽之計算效率。綜合以上所述，本計畫將結合廣義有限差分法、運算子拆解法、任意拉格朗日歐拉法、造波機、數值海綿消能層與繪圖卡平行計算，建立一個模擬黏性不可壓縮流體之三維平行化數值波浪水槽。本研究將考慮不同形式之海洋與海岸結構物對於入射波浪之影響，也將模擬前進波浪與不規格海床之互制問題，以及模擬海面固定浮體對前進波浪傳遞之影響等問題，本計畫之模擬結果與電腦模式可以提供給海洋工程、海岸工程、海洋能源與波浪理論研究參考。In this project, a three-dimensional numerical wave flume, based on the generalized finite difference method (GFDM) and the GPU parallel computation, will be developed to simulate the flow fields of incompressible viscous fluid. The moving-boundary problems of propagation of nonlinear water waves can be efficiently investigated by using the proposed numerical wave flume. It can be expected that the results and models of the project can be provided to academic research, engineering applications and scientific education in the future. Furthermore, the content of the proposed project is an extension of the projects in the past two years, but the working fluid in the present project is the incompressible viscous fluid instead of the potential flow. Although to consider the incompressible viscous fluid will tremendously increase difficulty in building the numerical model, the dynamic movements of real fluid flow can be really simulated and predicted. The GFDM, one of the newly-developed meshless methods, can truly get rid of time-consuming tasks of mesh generation and numerical quadrature, so the computational efficiency can be substantially improved. Besides, the GFDM is free from the troublesome problems of ill-conditioning matrix and free parameters, which usually accompany with other meshless methods. The GFDM with great efficiency, accuracy and stability is very suitable for developing numerical wave flume. In this project, the arbitrarily Lagrangian-Eulerian method is adopted to convert the Navier-Stokes equations, which are the governing equations for the incompressible viscous fluid, so the velocity and movements of computational nodes can be precisely considered. In addition, the GFDM and the operator-splitting scheme are responsible for the spatial and temporal discretizations, respectively. The numerical procedures are very simple and efficient by using the operator-splitting scheme, since the numerical procedures within one time step are reduced to three sequential steps and only one boundary value problem of Poisson equation should be analyzed. Besides, different wavemakers and numerical sponge layer are deployed along the inlet and outlet of the three-dimensional numerical wave flume so as to generate different incident waves and avoid any reflection from out-going waves. Finally, the GPU parallel computation is also added in the developed numerical wave flume, since the GFDM, the promising meshless method of collocation approach, is very suitable to cooperate with parallel computation. As a result, in this project, a three-dimensional numerical wave flume, based on the Navier-Stokes equations, are formed by adopting the GFDM, the arbitrarily Lagrangian-Eulerian method, the operator-splitting scheme, the wavemaker, the numerical sponge layer and the GPU parallel computation. By using the proposed numerical wave flume, several problems will be considered, such as the interactions between incident waves and marine structures, the influence on the wave characteristics by the irregular seabed, the force and moment on the fixed floating objects from the incident waves, etc. The outcomes of this project can be a reference for studies of marine engineering, coastal engineering, ocean energy and wave theorems.

Keyword(s)

廣義有限差分法
黏性不可壓縮流體
三維數值波浪水槽
無網格法
那維爾-史托克斯方程式
任意拉格朗日歐拉法
運算子拆解法
繪圖卡平行計算
Generalized finite difference method
incompressible viscous fluid
three-dimensional numerical wave flume
meshless method
Navier-Stokes equations
arbitrarily Lagrangian-Eulerian method
operator-splitting scheme
GPU parallel computation

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Using Generalized Finite Difference Method for Three-Dimensional Parallel-Computation Numerical Wave Flume Based on Viscous Incompressible Fluid

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