A combined algorithm between a segregated finite element method and a monotone streamline upwinding method for solving two-dimensional viscous incompressible thermal flows is presented. The finite element equations ar...
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A combined algorithm between a segregated finite element method and a monotone streamline upwinding method for solving two-dimensional viscous incompressible thermal flows is presented. The finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consists of the conservation of mass, momentums and energy. The method uses the three-node triangular element with equal-order interpolations for all the variables of the velocity components, the pressure and the temperature. The efficiency of the developed finite element formulation was evaluated by solving natural convection examples of the thermally driven flows in a square cavity and in concentric cylinders. The formulation was further evaluated by solving a forced convection example of a flow past a heated cylinder. In addition, an adaptive meshing technique is also implemented to further increase the solution accuracy, and at the same time, to minimize the computational time and computer memory requirement. (C) 2003 Elsevier B.V. All rights reserved.
A finite element method for analysis of two-dimensional, steady-state, viscous incompressible flow is presented. Finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consis...
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A finite element method for analysis of two-dimensional, steady-state, viscous incompressible flow is presented. Finite element equations are derived from a set of coupled nonlinear Navier-Stokes equations that consists of the conservation of mass and momentums. The convection terms in momentum equations are treated by streamline upwinding method to avoid the oscillation in the solution. The method has been developed for triangular element that employs equal-order interpolation functions for both the velocities and pressure. A segregated solution algorithm is also incorporated to compute the velocities and pressure separately. The method is combined with an adaptive meshing technique to further increase the solution accuracy, and at the same time, to minimize the computational time and computer memory requirement. The finite element formulation and the computer program have been verified by several examples that have known solutions prior to applying to solve more complex flow problems.
This paper presents a finite element method for the solution of 3D incompressible magneto hydrodynamic (MHD) flows. Two important issues are thoroughly addressed. First, appropriate formulations for the magnetic gover...
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This paper presents a finite element method for the solution of 3D incompressible magneto hydrodynamic (MHD) flows. Two important issues are thoroughly addressed. First, appropriate formulations for the magnetic governing equations and the corresponding weak variational forms are discussed. The selected (B, q) formulation is conservative in the sense that the local divergence-free condition of the magnetic field is accounted for in the variational sense. A Galerkin-least-squares variational formulation is used allowing equal-order approximations for all unknowns. In the second issue, a solution algorithm is developed for the solution of the coupled problem which is valid for both high and low magnetic Reynolds numbers. Several numerical benchmark tests are carried out to assess the stability and accuracy of the finite element method and to test the behavior of the solution algorithm. (C) 2001 Elsevier Science B.V. All rights reserved.
A segregated finite element algorithm for the solution of the SUPG formulation of the incompressible steady-state Navier-Stokes equations for non-isothermal flow is presented in this paper. The method features equal o...
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A segregated finite element algorithm for the solution of the SUPG formulation of the incompressible steady-state Navier-Stokes equations for non-isothermal flow is presented in this paper. The method features equal order interpolation for all the how variables. The SIMPLER and SIMPLEST algorithms are employed and the sets of non-symmetric linear equations are solved by means of the preconditioned conjugate gradient squared solver, whilst the preconditioned conjugate gradient solver is used to solve the sets of symmetric linear equations. Three cases are used as a basis for the study, i.e. the flow in a square cavity, the flow between parallel plates and natural convection in a square cavity. The effect that the choice of the values of the relaxation parameters has on the number of iterations which is needed to obtain a converged solution is investigated. In each case there is an optimum combination which is amongst others a function of the grid and the flow parameters. A non-optimum choice may lead either to an unnecessary number of iterations or the solution becoming unstable. From the results it is concluded that the method performs well when the optimum combination of the values for the relaxation parameters is used. However, much can still be done to improve the robustness of the method. (C) 2000 Published by Elsevier Science S.A. All rights reserved.
A segregated finite element algorithm for the solution of the SUPG formulation of the incompressible steady-state Navier-Stokes equations for non-isothermal flow is presented in this paper. The method features equal o...
详细信息
A segregated finite element algorithm for the solution of the SUPG formulation of the incompressible steady-state Navier-Stokes equations for non-isothermal flow is presented in this paper. The method features equal order interpolation for all the how variables. The SIMPLER and SIMPLEST algorithms are employed and the sets of non-symmetric linear equations are solved by means of the preconditioned conjugate gradient squared solver, whilst the preconditioned conjugate gradient solver is used to solve the sets of symmetric linear equations. Three cases are used as a basis for the study, i.e. the flow in a square cavity, the flow between parallel plates and natural convection in a square cavity. The effect that the choice of the values of the relaxation parameters has on the number of iterations which is needed to obtain a converged solution is investigated. In each case there is an optimum combination which is amongst others a function of the grid and the flow parameters. A non-optimum choice may lead either to an unnecessary number of iterations or the solution becoming unstable. From the results it is concluded that the method performs well when the optimum combination of the values for the relaxation parameters is used. However, much can still be done to improve the robustness of the method. (C) 2000 Published by Elsevier Science S.A. All rights reserved.
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