Multigrid Numerical Solutions of Non-Isothermal Laminar Recirculating Flows

1999 ◽  
Author(s):  
Marcelo J. S. de Lemos ◽  
Maximilian S. Mesquita
Keyword(s):  
Numerical Solutions ◽  
Rectangular Domain ◽  
Optimal Number ◽  
Computational Effort ◽  
Temperature Fields ◽  
Two Dimensional ◽  
Discretization Scheme ◽  
Multigrid Algorithm ◽  
Finite Volume Discretization ◽  
Velocity And Temperature Fields

Abstract The present work investigates the efficiency of the multigrid numerical method applied to solve two-dimensional laminar velocity and temperature fields inside a rectangular domain. Numerical analysis is based on the finite volume discretization scheme applied to structured orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different inlet Reynolds number (Rein) and number of grids. Up to four grids were used for both V- and W-cycles. Simultaneous and uncoupled temperature-velocity solution schemes were also applied. Advantages in using more than one grid is discussed. Results further indicate an increase in the computational effort for higher Rein and an optimal number of relaxation sweeps for both V- and W-cycles.

Effect of Permeability on Convergence Rates of Multigrid Solutions of Laminar Flows in Porous Media

2003 ◽  
Author(s):  
Maximilian S. Mesquita ◽  
Marcelo J. S. de Lemos
Keyword(s):  
Multigrid Method ◽  
Convergence Rates ◽  
Computational Effort ◽  
Laminar Flows ◽  
Two Dimensional ◽  
Multigrid Algorithm ◽  
Finite Volume Discretization ◽  
Medium Permeability ◽  
Correction Scheme ◽  
Grid Level

The present work investigates the efficiency of the multigrid method when applied to solve laminar flow in a two-dimensional tank filled with a porous material. The numerical method includes finite volume discretization with the flux blended deferred correction scheme on structure orthogonal regular meshes. Performance of the correction storage (CS) multigrid algorithm is compared for different numbers of sweeps in each grid level. Up to four grids, for both multigrid V- and W-cycles, are considered. Effects of medium permeability on converged rates are presented. Results indicate that W-cycles perform better in reducing the required computational effort and that the lower the permeability, faster solutions are obtained.

An asymptotic model of two-dimensional convection in the limit of low Prandtl number

1981 ◽  
Vol 102 ◽  
pp. 75-83 ◽  
Author(s):  
F. H. Busse ◽  
R. M. Clever
Keyword(s):  
Nusselt Number ◽  
Prandtl Number ◽  
Buoyancy Force ◽  
Close Agreement ◽  
Preceding Paper ◽  
Critical Value ◽  
Temperature Fields ◽  
Asymptotic Model ◽  
Two Dimensional ◽  
Velocity And Temperature Fields

An approximate solution of two-dimensional convection in the limit of low Prandtl number is presented in which the buoyancy force is balanced by the inertial terms. The results indicate that inertial convection becomes possible when the Rayleigh number exceeds a critical value of about 7 × 103. Beyond this value the velocity and temperature fields become independent of the Prandtl number except in thin boundary layers. The convective heat transport approaches the law Nu = 0·175 R¼ for the Nusselt number Nu. These results are in reasonably close agreement with the numerical results described in the preceding paper by Clever & Busse (1980).

Clocking Effects in a 1.5-Stage Axial Turbine: Boundary Layer Behaviour at Midspan

2004 ◽  
Author(s):  
Sven Ko¨nig ◽  
Axel Heidecke ◽  
Bernd Stoffel ◽  
Andreas Fiala ◽  
Karl Engel
Keyword(s):  
Boundary Layer ◽  
Shear Stress ◽  
Pressure Distribution ◽  
Static Pressure ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Discretization Scheme ◽  
Low Pressure Turbine ◽  
Finite Volume Discretization ◽  
Hot Film

This paper presents an experimental and numerical investigation on the influence of clocking on the boundary layer behaviour of the second stator in a 1.5-stage axial low pressure turbine. Surface mounted hot-film sensors were used to measure the quasi shear stress on the second stator and static pressure tappings to obtain the pressure distribution. All experiments were carried out at midspan for different clocking positions. The supporting numerical calculations were conducted with a two-dimensional Navier-Stokes solver using a finite volume discretization scheme and the v′2f turbulence model.

scholarly journals Hydro Magnetic Elastic Free Convection of a Conducting Elastico-Viscous Liquid Between Heated Vertical Plates

2009 ◽  
Vol 5 (2) ◽  
pp. 47-56
Author(s):  
P. Sreehari Reddy ◽  
A. S. Nagarajan ◽  
M. Sivaiah
Keyword(s):  
Magnetic Parameter ◽  
Numerical Solutions ◽  
Transverse Magnetic ◽  
Elastic Parameter ◽  
Temperature Fields ◽  
Convection Flow ◽  
Natural Convection Flow ◽  
Elastic Liquid ◽  
Velocity And Temperature Fields ◽  
Marine Engineering

The natural convection flow of a conducting visco-elastic liquid between two heated vertical plates under the influence of a    transverse magnetic field has been studied in this paper. Dimensionless equations of the problem have been solved by the method of successive approximation. Numerical solutions for velocity and temperature have been obtained. The results obtained are discussed with the help of graphs. The effect of magnetic parameter M, Visco-elastic parameter RC and the product of Prandtl and Eckert numbers [PE] on velocity and temperature fields are investigatedKey words: Visco-elastic liquid, viscous dissipation, vertical plates, convection, successive approximation.DOI: 10.3329/jname.v5i2.2694Journal of Naval Architecture and Marine Engineering 5(2)(2008) 47-56  

scholarly journals Numerical Solution of Two Dimensional Laplace’s Equation on a Regular Domain Using Chebyshev Differentiation Matrices

2019 ◽  
pp. 1-7
Author(s):  
M. O. Durojaye ◽  
J. K. Odeyemi ◽  
I. J. Ajie
Keyword(s):  
Finite Element ◽  
Finite Difference ◽  
Satisfactory Result ◽  
Numerical Solutions ◽  
Rectangular Domain ◽  
Two Dimensional ◽  
Laplace’S Equation ◽  
Regular Domain ◽  
Efficient Procedure ◽  
Laplace's Equation

This work presents an efficient procedure based on Chebychev spectral collocation method for computing the 2D Laplace’s equation on a rectangular domain. The numerical results and comparison of finite difference and finite element methods are presented. We obtained a satisfactory result when compared with other numerical solutions.

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