Two-level Newton iterative method for the 2D/3D steady Navier-Stokes equations

2011 ◽  
Vol 28 (5) ◽  
pp. 1620-1642 ◽  
Author(s):  
Yinnian He ◽  
Yan Zhang ◽  
Yueqiang Shang ◽  
Hui Xu
Keyword(s):  
Iterative Method ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Newton Iterative Method

A PRIORI PRESSURE FIELD CONSTRUCTION ITERATIVE METHOD FOR THE SOLUTION OF THE STEADY-STATE NAVIER–STOKES EQUATIONS USING GENERAL FINITE-VOLUME CO-LOCATED GRIDS

2007 ◽  
Vol 04 (04) ◽  
pp. 567-601
Author(s):  
JOSE A. LAMAS
Keyword(s):  
Iterative Method ◽  
Pressure Field ◽  
Stokes Equations ◽  
A Priori ◽  
Mass Conservation ◽  
Momentum Conservation ◽  
Navier Stokes ◽  
Pressure Equation ◽  
Navier Stokes Equations ◽  
Correction Equations

An iterative method has been developed for the solution of the Navier–Stokes equations and implemented using finite volumes with co-located variable arrangement. A pressure equation is obtained combining algebraic momentum and mass conservation equations resulting in a self-consistent set of equations. An iterative procedure solves the pressure equation consistently with mass conservation and then updates velocities based on momentum equations without introducing velocity or pressure correction equations. The process is repeated until velocities satisfy both mass and momentum conservation. Tests demonstrate a priori pressure field solution consistent with mass conservation, and solution of hydrostatic problems in one iteration.

Study Method for Low Speed Flow Basic on Precondition

2014 ◽  
Vol 1070-1072 ◽  
pp. 1972-1977
Author(s):  
Lang Li ◽  
Guo Ping Cheng ◽  
Guo Quan Zhu ◽  
Wei Zhang
Keyword(s):  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Speed Flow ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The Results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field ,All these works built foundations for further application of chemical flows.

Low-Speed Preconditioning for AUSM+-Up Scheme

2015 ◽  
Vol 723 ◽  
pp. 224-228
Author(s):  
Wei Peng ◽  
Guo Ping Chen ◽  
Lang Li
Keyword(s):  
Flow Field ◽  
Iterative Method ◽  
Stokes Equations ◽  
Time Derivative ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Low Speed ◽  
Preconditioning Method ◽  
Derivative Term ◽  
Implicit Iterative Method

Based on Navier-stokes equations, Weiss-Smith matrix preconditioning method is implemented within pseudo time derivative term. AUSM+-up family schemes and LU-SGS implicit iterative method were used to solve low speed flows and were compared with literature data and theoretical value. Through comparing calculation with the literature data and theoretical value, The results showed the preconditioning algorithm can be applied efficiently to the low speeds flow field, All these works built foundations for further application of chemical flows.

scholarly journals AN ITERATIVE METHOD FOR THE NAVIER-STOKES EQUATIONS IN THE PROBLEM OF A VISCOUS INCOMPRESSIBLE FLUID FLOW AROUND A THIN PLATE

2020 ◽  
pp. 132-142
Author(s):  
M.A. Sumbatyan ◽  
◽  
Ya.A. Berdnik ◽  
A.A. Bondarchuk ◽  
◽  
...  
Keyword(s):  
Integral Equation ◽  
Fluid Flow ◽  
Iterative Method ◽  
Thin Plate ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Iteration Step ◽  
Navier Stokes ◽  
Large Reynolds Number ◽  
Navier Stokes Equations

In this paper, the problem on a viscous fluid flow around a thin plate is considered using the exact Navier–Stokes equations. An iterative method is proposed for small velocity perturbations with respect to main flow velocities. At each iterative step, an integral equation is solved for a function of the viscous friction over the plate. The collocation method is used at each iteration step to reduce an integral equation to a system of linear algebraic equations, and the shooting method based on the classical fourth-order Runge-Kutta technique is applied. The solution obtained at each iteration step is compared with the Harrison–Filon solution at low Reynolds numbers, with the classical Blasius solution, and with the results computed using the direct numerical finite-volume method in the ANSYS CFX software for moderate and high Reynolds numbers. The proposed iterative method converges in a few steps. Its accuracy is rather high for small and large Reynolds number, while the error can reach 15% for moderate values.

Sign in / Sign up

Export Citation Format

Share Document