A finite difference method for solving unsteady viscous flow problems

AIAA Journal ◽  
1985 ◽  
Vol 23 (5) ◽  
pp. 659-668 ◽  
Author(s):  
C. P. Li
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Viscous Flow ◽  
Difference Method ◽  
Flow Problems ◽  
Unsteady Viscous Flow

scholarly journals Semi-Analytical Solution of Two-Dimensional Viscous Flow through Expanding/Contracting Gaps with Permeable Walls

2021 ◽  
Vol 26 (2) ◽  
pp. 41
Author(s):  
Mohammad Mehdi Rashidi ◽  
Mikhail A. Sheremet ◽  
Maryam Sadri ◽  
Satyaranjan Mishra ◽  
Pradyumna Kumar Pattnaik ◽  
...  
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Viscous Flow ◽  
Numerical Method ◽  
Asymptotic Method ◽  
Difference Method ◽  
Series Form ◽  
Advantages And Disadvantages ◽  
Adomian Decomposition ◽  
In Series

In this research, the analytical methods of the differential transform method (DTM), homotopy asymptotic method (HAM), optimal homotopy asymptotic method (OHAM), Adomian decomposition method (ADM), variation iteration method (VIM) and reproducing kernel Hilbert space method (RKHSM), and the numerical method of the finite difference method (FDM) for (analytical-numerical) simulation of 2D viscous flow along expanding/contracting channels with permeable borders are carried out. The solutions for analytical method are obtained in series form (and the series are convergent), while for the numerical method the solution is obtained taking into account approximation techniques of second-order accuracy. The OHAM and HAM provide an appropriate method for controlling the convergence of the discretization series and adjusting convergence domains, despite having a problem for large sizes of obtained results in series form; for instance, the size of the series solution for the DTM is very small for the same order of accuracy. It is hard to judge which method is the best and all of them have their advantages and disadvantages. For instance, applying the DTM to BVPs is difficult; however, solving BVPs with the HAM, OHAM and VIM is simple and straightforward. The extracted solutions, in comparison with the computational solutions (shooting procedure combined with a Runge–Kutta fourth-order scheme, finite difference method), demonstrate remarkable accuracy. Finally, CPU time, average error and residual error for different cases are presented in tables and figures.

scholarly journals Finite Difference Method for Solving a System of Third-Order Boundary Value Problems

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Muhammad Aslam Noor ◽  
Eisa Al-Said ◽  
Khalida Inayat Noor
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Boundary Value Problems ◽  
Difference Method ◽  
Boundary Value ◽  
Approximate Solutions ◽  
Obstacle Problems ◽  
Third Order ◽  
Flow Problems ◽  
Coating Flow

We develop a new-two-stage finite difference method for computing approximate solutions of a system of third-order boundary value problems associated with odd-order obstacle problems. Such problems arise in physical oceanography (Dunbar (1993) and Noor (1994), draining and coating flow problems (E. O. Tuck (1990) and L. W. Schwartz (1990)), and can be studied in the framework of variational inequalities. We show that the present method is of order three and give numerical results that are better than the other available results. Numerical example is presented to illustrate the applicability and efficiency of the new method.

Sign in / Sign up

Export Citation Format

Share Document