Streamline-upwind Method Research Articles

Equal Low-Order Finite Element Simulation of the Planar Contraction Flow for Branched Polymer Melts

The rheological characteristics of branched polymer melts is described by the modified XPP model, which is discretized by inconsistent streamline-upwind method. A finite increment calculus procedure is introduced to reformulate the mass equation and to overcome oscillations of the pressure field. Moreover, the governing equations are discretized and solved by the iterative fractional step algorithm. Thus the equal low-order finite elements for velocity-pressure-stress variables are adopted to calculate the planar contraction viscoelastic flows. The influences of the Weissenberg number and the amount of branched-arms on the rheological behavior of the Pom-Pom molecule are discussed. Results demonstrate good agreement with those given in the literatures.

Characteristic based split (CBS) meshfree method modeling for viscoelastic flow

A semi-implicit characteristic based split meshfree algorithm is proposed for the numerical solution of incompressible viscoelastic flow in the paper, in which the governing equations are discretized by element free Galerkin method in spatial space and the characteristic based split method is adopted in temporal space. In order to obtain stable and convergent solution at high Weissenberg number, streamline upwind method is chosen to tackle the convective terms in constitutive equations of viscoelastic flow. Meanwhile, mass lumped technique is adopted to accelerate computational efficiency. The method allows the equal order basis to approximate pressure, velocity and extra stress, especially the linear basis that is easy to implement. The planar Poiseuile flow and 4:1 planar contraction flow for an Oldroyd B fluid are investigated. Through these numerical experiments, we find that the method has good stability and the numerical results are in agreement well with those reported by other papers.

Two-dimensional non-stationary numerical model for MSM structures

In this paper the solution of the non-stationary model for MSM structures is obtained numerically. The two-dimensional model consists of three singularly perturbed non-linear partial differential equations. The alternating-direction method for discretization in time and the non-oscillatory streamline upwind method on a piecewise uniform grid for discretization in space are used to eliminate the interior and boundary layer oscillations. The described model is used for the analysis of the time response of a GaAs n-type MSM structure to a Heaviside function form of the applied voltage. For the stationary case the I–V characteristic of the structure is determined. The numerical results confirm that the applied method is convenient for solving convection–diffusion problems. Copyright © 1999 John Wiley & Sons, Ltd.

Streamline Upwind Finite-Element Method for Overland Flow

A streamline upwind, finite-element method is proposed to solve the two-dimensional (2D) kinematic wave and shallow water wave equations for overland flow problems. The spatial domain is discretized into a network of quadrilateral, bilinear finite elements, and time derivatives are treated by a three-point finite-difference scheme to increase numerical stability. Solutions computed by the streamline upwind method are compared to those of the Galerkin method. Streamline upwind and Galerkin solutions of the kinematic wave equation exhibited good agreement with an analytic solution for flow over an inverted cone. However, the Galerkin solution exhibited oscillations during the steady portion of the runoff hydrograph. Galerkin solutions of the shallow water wave equations for inverted cone and bowl-shaped surfaces displayed oscillations in time and space, while the streamline upwind method exhibited no oscillatory behavior. Results generated by the streamline upwind method agreed well with experimental data sets and simulations conducted with the MacCormack finite-difference method.

New Hybrid-Streamline-Upwind Finite-Element Method for a Dual Space. Verification for Two-Dimensional Advection-Diffusion Equation.

We have proposed a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method, and verified that this method is valid at high Reynolds numbers for unsteady problems using a one-dimensional Burgers equation. In this paper, we will show that this method is valid for steady two-dimensional advection-diffusion problems. Examples demonstrate the effectiveness of this streamline-upwind method for a dual space, excluding both wiggles and spurious crosswind diffusion which afflict some classical upwind schemes. Furthermore we achieve a simple formulation and high-speed calculation using the finite-element method, by combining the advection term and the diffusion term.

New Hybrid-Streamline-Upwind Finite-Element Method in A Dual Space. 3rd Report, Verification for Two-Dimensional Advection-Diffusion Equation.

We have proposed a new hybrid-streamline-upwind finite-element method, which is based on the finite analytic method developed in the field of the finite difference method, and verified that this method is valid at high Reynolds numbers for unsteady one-dimensional Burgers equation problems. In this paper, we will show that this method is valid for steady two-dimensional advection-diffusion problems. Examples demonstrate the effectiveness of this streamline-upwind method in excluding both wiggles and the spurious crosswind diffusion that afflicts some classical upwind schemes. Furthermore we achieve simplicity of formulation and high-speed calculation of the finite-element method, putting advection term and diffusion term together.

A monotone streamline upwind method for quadratic finite elements

AbstractA direct streamline upwind method has been developed for convection‐dominated flow problems utilizing quadratic elements. The approach presented retains the curve‐sidedness feature offered by these elements. This facilitates the use of boundary conforming elements in domains that possess extreme curvature such as turbomachinery bladed components, for which the method is particularly suited. Three test cases are solved to evaluate the stability and diffusive characteristics of the numerical solution. The results presented clearly demonstrate that the proposed method does not exhibit any non‐physical spatial oscillations, nor does it suffer from the traditional problem of excessive numerical diffusion.

The simultaneous use of 4�4 and 2�2 bilinear stress elements for viscoelastic flows

Mixed finite elements for viscoelastic flows based on a 4×4 sub-linear interpolation for the extra stress components satisfy the Babuska-Brezzi condition and are highly stable. They have been proved to be quite satisfactory in solving problems with strong stress boundary layers. In this work, we examine the simultaneous use of 4×4 and 2×2 bilinear stress elements in an attempt to reduce the computational cost without sacrificing the accuracy. The 4×4 bilinear elements are employed in regions where the stress field is anticipated to be steep while the 2×2 elements carry the burden elsewhere with a much smaller number of stress nodes. Additional constraints along the sides shared by different elements are necessary in order to preserve conformity. The method is applied to the creeping flow of a Maxwell fluid around a sphere falling along the axis of a cylindrical tube. Results are given for three mixed finite element formulations: the Galerkin method, the consistent streamline-upwind/Petrov-Galerkin method (SUPG) and the non-consistent streamline-upwind method (SU). Particular emphasis is given on the calculated drag correction factors. The effect of the sphere/cylinder diameter ratio is also examined.

Numerical Simulation of Contraction Flow for Viscoelastic Fluids at High Weissenberg Number by the Streamline-Upwind Finite Element Method

Numerical simulation of viscoelastic flow at high Weissenberg number (We) was carried out by the streamline-upwind finite element method with the sub-elements for stress components proposed by Marchal and Crochet. This method and the Galerkin finite element method were applied to the stick-slip flow with the singular point in order to examine the effectiveness of this method. The Oldroyd-B model was used as a constitutive equation. This model incorporates strong elasticity and numerical solutions sometimes diverge. When the Galerkin finite element method was used, the numerical solutions had oscillation and the loss of convergence occurred at relatively low value of We. On the other hand, when the streamline-upwind method was used with the stress sub-elements, the oscillation of numerical solutions did not appear and the solution could be obtained up to a high value ofWe. Using the latter method, the calculation of the tapered contraction flow was carried out with the Giesekus model as a constitutive equation. The limit values of We were not encountered and we could calculate even at We> 100 using various values of model parameters. It was concluded that the streamline-upwind finite element method with the stress sub-elements was very useful to simulate the contraction flow up to high values of We.