Application of Be/Ge Embedded Local Collocation Method to the Simulation of 2d Vortical Flows

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Project title

Code/計畫編號

MOST109-2221-E415-009

Translated Name/計畫中文名

嵌入式局部多項式配點法於二維渦漩流場模擬之應用研究

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

https://www.grb.gov.tw/search/planDetail?id=13552007

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-07-2021

Bugetid/研究經費

504千元

ResearchField/研究領域

土木水利工程

本研究將應用嵌入式局部多項式配點法於二維渦漩流場之數值模擬。若干文獻提及，強式無網格法在做配點時，若能讓控制方程式和邊界條件在邊界點那邊同時被滿足，則可提高數值穩定，並得到較準確之計算結果。依此概念，Wu and Tsay (2013)提出利用懲罰權重來將控制方程式及邊界條件嵌入局部近似中。此方法雖已被應用於求解若干二維及三維的邊界值問題，但至今仍未被廣泛應用，也未被應用於黏性流場之數值模擬上面。本計畫將做這方面的嘗試。利用時間上之微小增加，二維不可壓縮流場問題可簡化為每個時間步各是一個邊界值問題，恰好可利用嵌入式局部配點法求解之，然後用求解的結果預測下個時間步的流場，如此可一直計算下去。將以若干個經典的二維渦漩問題來驗證數值計算結果。 In this study, we will employ the BC/GE embedded local polynomial collocation method to the simulation of 2D viscous flows. It was stated in literatures that making the governing equation satisfied at boundary points as well as the boundary conditions are can improve numerical stability and accuracy in strong form meshless methods. Following this concept, Wu and Tsay (2013) proposed a new meshless method. Though the method of Wu and Tsay (2013) has been employed to solve several 2D and 3D boundary value problems, it is still not widely known. As a first try of employing this method to the simulation of viscous flows, the focus of this study is on the simulation of 2D vortices only. With a small time increment, the 2D incompressible viscous flow is separated as a series of well posed boundary value problems at discrete time instants. At each time step, the well posed boundary value problem is solved numerically. The obtained solutions are then used to predict the flow velocities and vorticities in further time steps. We will choose some benchmark problems to verify the numerical results.

Keyword(s)

無網格
局部多項式
配點
加權最小二乘法
二維渦漩
Meshless
local polynomial
collocation
weighted-least-squares
2D vortex

DSpace CRIS

Application of Be/Ge Embedded Local Collocation Method to the Simulation of 2d Vortical Flows

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