Application of Local Polynomial Collocation Method to the Simulation of Pressure Distribution beneath Non-Linear Water Waves

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Project title

Code/計畫編號

MOST105-2221-E415-008

Translated Name/計畫中文名

以局部多項式配點法模擬非線性水波下壓力分佈之研究

Project Coordinator/計畫主持人

Nan-Jing Wu

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Civil and Water Resources Engineering,NCYU

Website

grb.gov.tw/search/planDetail?id=11877267

Year

2016

Start date/計畫起

01-08-2016

Expected Completion/計畫迄

31-07-2017

Bugetid/研究經費

617千元

ResearchField/研究領域

土木水利工程

本計晝將延續科技部專題研究計晝「非線性水波三維無網格數值模式之發展與應用（II)」之研究成果，將三維非線性自由液面勢流流場之無網格數值模式，更新為能夠直接計算壓力場之模式。依據相關文獻之記載，不可壓縮流體之動力方程式，不論有無考慮黏滯力，均可推導出一條與速度變化歷程無關之卜桑方程式，這條方程式能描述各個瞬時的壓力變化。Wu et al.(2015)在其論文中，先計算自由液面勢流流場，得到速度向量各分量的速度梯度，然後再求解這一條壓力方程式，成功地計算出矩形水槽在水平搖晃時水槽内液體壓力的分佈。本研究將基於這個結果，重新構想出一套演算法，直接求解這條壓力方程式，然後由壓力梯度計算流體加速度，再進一步追蹤流體質點之執跡。這個模擬在水波模擬之應用上將會更快更有效率。而且，計算結果能直接呈現水中構造物表面之壓力分佈，在工程分析與設計上，更具實用意義。而求解壓力方程式的核心數值方法，仍是Wu and Tsay (2013)提出之局部多項式配點法。 In this project, we will continue the research on the “Development and Application of the Three-Dimensional Mesh-free Numerical Model for Nonlinear Water Waves (II).” The 3-D mesh-free numerical model for the simulation of pressure distribution beneath the fully nonlinear free surface will be will be established. This model will be the upgrade version of our previous model which is for the free surface potential flow simulations. According to the text book of turbulent flows (Pope, 2000), the momentum equation of incompressible flow can be reduced to a Poisson equation governing the pressure distribution, no matter the viscous effect is considered or not. Following this, Wu et al. (2015) used their numerical results of the free surface potential flow simulation to obtain the pressure distribution in a rectangular swaying tank. Based on this, we will propose a new algorithm. After solving this pressure equation, the pressure gradient in the flow field and then the accelerations of fluid particles will be obtained. Thus the trajectories of fluid particles are accurately estimated and the movement of the free surface is precisely predicted. Because the pressure equation is directly solved in this model, the results include the pressure distribution on solid body surfaces. This is applicable for engineering analysis and design. The method for solving the pressure equation is the local polynomial collocation method prosed by Wu and Tsay (2013).

Keyword(s)

局部多項式配點法
無網格
流體質點追蹤
local polynomial collocation method
mesh-free
particle tracking

DSpace CRIS

Application of Local Polynomial Collocation Method to the Simulation of Pressure Distribution beneath Non-Linear Water Waves

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