Developments of Meshless Numerical Model for Three-Dimensional Flow Field of Viscous Incompressible Fluid by Using Stream-Function Vector Formulation

瀏覽統計 Email 通知 RSS Feed

簡歷

基本資料

Project title

Code/計畫編號

MOST109-2221-E019-005

Translated Name/計畫中文名

基於流線向量方程式開發三維不可壓縮黏性流體之無網格法電腦模擬模式

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=13544312

Year

2020

Start date/計畫起

01-08-2020

Expected Completion/計畫迄

31-07-2021

Bugetid/研究經費

564千元

ResearchField/研究領域

土木水利工程

本計畫採用亥姆霍茲定律推導流線向量方程式，將原始變數方程式型態的納維爾史托克斯方程式轉換為流線向量方程式，可以避免壓力邊界條件未定的困擾；並採用流線向量方程式建立模擬三維不可壓縮黏性流體之無網格法電腦模擬模式，採用數個三維穩態與非穩態不可壓縮黏性流場進行電腦模擬分析，並將結果與其他數值結果及實驗結果進行比較，以證明所開發電腦模擬模式的優異性。採用亥姆霍茲定律可以將速度向量表示為一個無旋度向量與一個無散度向量的線性累加，在三維的流場問題中，控制方程式為四條四階非線性偏微分方程組，且未知變數為流線向量與勢能函數共四個變數，相較於納維爾史托克斯方程式的其他表示形式，流線向量方程式是非常具有競爭優勢的。本計劃採用廣義有限差分法求解推導得之流線向量方程式，廣義有限差分法是一種新發展的無網格法，可以避免建立網格與數值積分的耗時工作，可以大幅減少電腦模擬時間，也可以簡化所撰寫的程式；此外，廣義有限差分法可以求解任意型態之偏微分方程組，非常適合用於求解流線向量方程式。本計劃將採用廣義有限差分法分析流線向量方程式，建立一個簡易、高準確性、高穩定性與高計算效率之三維不可壓縮黏性流體流場的電腦模擬模式。In this project, the primitive-variable formulation of the Navier-Stokes equations is transformed to the steam-function vector formulation by using the Helmholtz decomposition theorem. To adopt the steam-function vector formulation can ovoid the troublesome task of determination of the boundary conditions for pressure. The stream-function vector formulation is adopted to form a meshless computer simulation model for three-dimensional flow fields of incompressible viscous fluid. In addition, several numerical examples of steady and unsteady flow fields are adopted to verify the merits of the proposed model. The numerical results will be compared with other published numerical solution and experimental data to examine the accuracy, stability and consistency of the proposed computer model. The velocity vector is expressed as a linear combination of a curl-free vector and a divergence-free vector when the Helmholtz decomposition theorem is used. For three-dimensional flow fields, the governing equations are a system of four nonlinear fourth-order partial differential equations with four dependent variables, which include the stream-function vector and a scalar potential function. Consequently, the stream-function vector formulation is extremely competitive in comparison with other formulations of the Navier-Stokes equations from the viewpoint of computational efficiency. In this project, the generalized finite difference method (GFDM), one kind of newly-developed meshless methods, is adopted to efficiently solve the stream-function vector formulation. The GFDM is truly free from mesh generation and numerical quadrature, so to use the GFDM can increase the efficiency of computer simulation and simplify the task of programming code. Besides, the GFDM, which can solve various type of partial differential equations, is very suitable for solving the stream-function vector formulation. As a result, in this project, the GFDM is adopted to efficiently and accurately analyze the stream-function vector formulation and the resultant computer simulation model will be very simple, highly accurate, extremely stable and quite efficient for three-dimensional flow fields of incompressible viscous fluid.

Keyword(s)

流線向量方程式
亥姆霍茲定律
納維爾史托克斯方程式
不可壓縮黏性流體
三維流場
無網格法
廣義有限差分法
Stream-function vector formulation
Helmholtz decomposition theorem
Navier-Stokes equations
incompressible viscous fluid
three-dimensional flow field
meshless methods
generalized finite difference method

DSpace CRIS

Developments of Meshless Numerical Model for Three-Dimensional Flow Field of Viscous Incompressible Fluid by Using Stream-Function Vector Formulation

基本資料

Description