Constructing the Numerical Method for Navier — Stokes Equations Using Computer Algebra System

2005 ◽  
pp. 367-378 ◽  
Author(s):  
Leonid Semin ◽  
Vasily Shapeev
Keyword(s):  
Numerical Method ◽  
Computer Algebra ◽  
Computer Algebra System ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations

Validation of a Numerical Method for Unsteady Flow Calculations

1993 ◽  
Vol 115 (1) ◽  
pp. 110-117 ◽  
Author(s):  
M. Giles ◽  
R. Haimes
Keyword(s):  
Heat Transfer ◽  
Flat Plate ◽  
Numerical Method ◽  
Stokes Equations ◽  
Companion Paper ◽  
Ideal Gas ◽  
Euler Method ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Loss Prediction

This paper describes and validates a numerical method for the calculation of unsteady inviscid and viscous flows. A companion paper compares experimental measurements of unsteady heat transfer on a transonic rotor with the corresponding computational results. The mathematical model is the Reynolds-averaged unsteady Navier–Stokes equations for a compressible ideal gas. Quasi-three-dimensionality is included through the use of a variable streamtube thickness. The numerical algorithm is unusual in two respects: (a) For reasons of efficiency and flexibility, it uses a hybrid Navier–Stokes/Euler method, and (b) to allow for the computation of stator/rotor combinations with arbitrary pitch ratio, a novel space–time coordinate transformation is used. Several test cases are presented to validate the performance of the computer program, UNSFLO. These include: (a) unsteady, inviscid flat plate cascade flows (b) steady and unsteady, viscous flat plate cascade flows, (c) steady turbine heat transfer and loss prediction. In the first two sets of cases comparisons are made with theory, and in the third the comparison is with experimental data.

scholarly journals Numerical simulation of cavitating two-phase gas-liquid three-dimensional flow in a duct of varying cross-section based on homogenous mixture model

2006 ◽  
Vol 28 (3) ◽  
pp. 134-144
Author(s):  
Nguyen The Duc
Keyword(s):  
Numerical Simulation ◽  
Numerical Method ◽  
Cross Section ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Grid Systems ◽  
Curvilinear Grid

The paper presents a numerical method to simulate two-phase turbulent cavitating flows in ducts of varying cross-section usually faced in engineering. The method is based on solution of two-phase Reynolds-averaged Navier-Stokes equations of two-phase mixture. The numerical method uses artificial compressibility algorithm extended to unsteady flows with dual-time technique. The discreted method employs an implicit, characteristic-based upwind differencing scheme in the curvilinear grid systems. Numerical simulation of an unsteady three-dimensional two-phase cavitating flow in a duct of varying cross-section with available experiment was performed. The unsteady important characteristics of the unsteady flow can be observed in results of numerical simulation. Comparison of predicted results with experimental data for time-averaged velocity and phase fraction are provided.

Computations of Ship Stern and Wake Flow and Comparisons with Experiment

1990 ◽  
Vol 34 (03) ◽  
pp. 179-193
Author(s):  
V. C. Patel ◽  
H. C. Chen ◽  
S. Ju
Keyword(s):  
Experimental Data ◽  
Shear Flow ◽  
Numerical Method ◽  
Stokes Equations ◽  
Ship Hull ◽  
Wake Flow ◽  
Navier Stokes ◽  
Turbulent Shear ◽  
Turbulent Shear Flow ◽  
Navier Stokes Equations

A numerical method for the solution of the Reynolds-averaged Navier-Stokes equations has been employed to study the turbulent shear flow over the stern and in the wake of a ship hull. Detailed comparisons are made between the numerical results and available experimental data to show that most of the important overall features of such flows can now be predicted with considerable accuracy.

Sign in / Sign up

Export Citation Format

Share Document