A Domain Extension Approach in Radial Basis Function Collocation Methods Applied to Hydrodynamic Problems in Irregular Domains

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Project title

Code/計畫編號

NSC96-2221-E019-051-MY3

Translated Name/計畫中文名

徑基底函數選點法結合領域擴充策略在具不規則幾何領域中之水動力問題的應用

Project Coordinator/計畫主持人

Jiahn-Horng Chen

Funding Organization/主管機關

National Science and Technology Council

Department/Unit

Department of Systems Engineering and Naval Architecture

Website

https://www.grb.gov.tw/search/planDetail?id=1756122

Year

2009

Start date/計畫起

01-08-2009

Expected Completion/計畫迄

01-07-2010

Bugetid/研究經費

579千元

ResearchField/研究領域

機械工程

" 在本研究計畫申請書中，我們提出領域擴充法，運用徑基底函數選點法來解析在任意物理領域下的水動力問題，以解決目前文獻中所發展的徑基底函數選點無網格法力有未逮之瓶頸問題。在領域擴充的策略中，任意或複雜物理幾何領域將擴充成拓樸學上相當於矩形的領域，我們假設在此擴展的虛假領域中，原物理方程式仍成立，而相關的物理邊界條件則仍設定於原物理領域的邊界上。如此擴展之後的物理問題，將變成病態問題，但在選點法下，我們可藉由相關的方法來克服，而求得相關的數值解。我們認為領域擴充策略將可有效解決目前一般性的任意物理幾何形狀難題，也就是說，這是一個一般性的策略，而非僅侷限於某些特例的方法，同時整個解析流程則是比較簡單、有效率、並具強健性。整個計畫將分三年執行，第一年將探討領域擴充法的基礎問題及其理論依據；第二年將把第一年的成果應用於水動力學問題的解析，數值計算的範圍包括幾何形狀不規則的二維勢流場與黏性流場，兩者均涵蓋內流場與外流場。第三年的規劃則是整合前兩年的經驗，把領域擴充法結合其他相關的數值計算技巧，探討無網格法的兩個重要卻困難重重的應用課題，即大領域的二維流場問題與三維勢流場問題。表 " " A fictitious domain extension approach is proposed to study the hydrodynamic problems in arbitrary domains by the radial basis function collocation method. The main purpose of the proposal is to resolve one of the bottleneck problems encountered in the development of radial basis function collocation method applied to problems with irregular domains. In this approach, arbitrary physical geometries are extended to domains which are topologically rectangular. The solution domain is also extended to the fictitious area and assumed to satisfy the same governing equation in it and on its boundaries. The physical boundary conditions are still specified on the boundaries of the physical domain. The problem in the extended domain becomes ill-posed. However, it can be easily circumvented by the collocation method. We believe that the strategy of domain extension is a general approach which is applicable to hydrodynamic problems in any irregular flow domains. In addition, the analysis process will be simple, efficient and robust. In this proposal, we plan a series of work which will be carried out in three years. In the first year, we investigate the fundamental problems associated with the domain extension and the theoretical background which supports the strategy. These must be first studied so that the solid foundation can be laid for the new approach. In the second year, we will apply what is achieved in the first year to computations of hydrodynamic problems. The problems which will be studied include typical 2-D potential and viscous flows. Both internal and external flows will be tested. In the last year, we will combine the domain extension approach with other appropriate numerical techniques to study two difficult topics in applications of radial basis function collocation meshless methods. They are the 2-D hydrodynamic problem in large arbitrary domains and the 3-D potential flow problem. Some typical benchmark tests for typical flows will be carried out. "

Keyword(s)

選點法
徑基底函數
領域擴充法
複雜領域
水動力學問題
collocation method
radial basis function
domain extension
complicatedgeometry
hydrodynamics

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A Domain Extension Approach in Radial Basis Function Collocation Methods Applied to Hydrodynamic Problems in Irregular Domains

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