The Method of Particular Solutions for Solving the Convection-Diffusion Equation

View Statistics Email Alert RSS Feed

Information

Details

Project title

Code/計畫編號

NSC98-2221-E019-057

Translated Name/計畫中文名

以特解法求解對流擴散方程式

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=1915779

Year

2009

Start date/計畫起

01-08-2009

Expected Completion/計畫迄

31-07-2010

Bugetid/研究經費

363千元

ResearchField/研究領域

土木水利工程

"本計畫預期以新發展之特解法求解並分析穩態與暫態之對流擴散方程式。對流擴散方程式常用於描述廣泛的物理問題，例如：地下水中污染物的傳輸現象、以及流體運動方程式中的動量守恆與能量守恆方程式等。此一偏微分方程式用於描述對流項與擴散項之平衡，因此使用傳統數值計算方法不易準確計算出答案。因此本計畫預計以一種新的無網格數值計算方法來求解並分析對流擴散方程式。特解法是本計畫所採用的數值計算方法，此一新的數值方法不需要建立網格也不需要做數值積分，因此減少了電腦資源的需求量與人力的消耗；並且此特解法具有高精準度與快速收斂的特性，具有工業應用的潛力。所以本計畫預計以特解法分析對流擴散方程式，並測試數值方法中的幾種因素對於答案正確性的影響程度，並且將其應用在地下水污染等實際問題上。""In this project, the method of particular solutions is developed for solving and analyzing the steady and unsteady convection-diffusion equations. The convection-diffusion equation can be used to describe many practical problems, such as the transport of the pollution in groundwater, the momentum equations and energy equations in the Navier-Stokes equations, etc. This partial differential equation depicts the balance between the convective and diffusive terms; hence, it is difficult to accurately simulate the problem by conventional numerical methods. Therefore, we propose to use a newly-developed meshless method, which is the method of particular solutions, to analyze the convection-diffusion equations. This method is free from mesh generation and numerical integration, so it will greatly reduce the computer resource required. Besides, the method of particular solutions is a very accurate and fast convergent method in comparing with mesh-dependent numerical schemes. So, we will apply this method of particular solutions for solving the convection-diffusion equation. And several factors that might influence on the accuracy of numerical results will be thoroughly examined. Furthermore, this numerical scheme will be tested on the problems of pollutant transport in groundwater."

Keyword(s)

特解法
對流擴散方程式
無網格數值計算方法
地下水污染
the method of particular solutions
convection-diffusion equation
meshlessmethod
pollutant transport in groundwater

DSpace CRIS

The Method of Particular Solutions for Solving the Convection-Diffusion Equation

Details

Description