Streamline-upwinding Finite Element Method Research Articles

Benchmarking a reduced order finite element method for multiphase carbon sequestration models

Carbon sequestration in deep saline aquifers has been proposed for long-term storage of CO2 as an alternative to the release of CO2 into the atmosphere. In this article, we present a computationally efficient numerical model based on a sequentially coupled Finite Element Method (FEM) and Streamline Upwind Finite Element Method (SU-FEM)-Finite Difference Method (FDM). An adaptive timestep strategy is implemented which allows computationally efficient and stable solutions as time progresses. The computational efficiency of the formulation is demonstrated by four examples that consider nonuniform permeability, multiple injection wells, an upsloping aquifer, and a dome-shaped aquifer. The adaptive timesteps reduce the computational cost by 75-82% compared to constant timesteps in the four examples considered. The proposed formulation is compared against a benchmark study where eleven different simulators were used to determine the arrival time of the CO2 plume at a leaky well. The original benchmark study did not include an FEM-based discretization of the reduced order equations. To the authors’ best knowledge, the current work is the first FEM based implementation of reduced order (vertically averaged) multiphase flow equations evaluated against this benchmark. The proposed formulation is in good general agreement with the results from the various simulators studied in the benchmark, and excellent agreement with an FDM discretization of the vertically averaged governing equations.

Characteristic Tailored Finite Point Method for Convection-Dominated Convection-Diffusion-Reaction Problems

In this paper, we propose a characteristic tailored finite point method (CTFPM) for solving the convection-diffusion-reaction equation with variable coefficients. We develop an algorithm to construct a streamline-aligned grid for the CTFPM. Our numerical tests show for small diffusion coefficient the CTFPM solution resolves the internal and boundary layers regardless the mesh size, and depicts that CTFPM method with a streamline grid has excellent performance compared with the tailored finite point method and a streamline upwind finite element method when ? is small.

Streamline upwind finite element method using 6-node triangular element with adaptive remeshing technique for convective-diffusion problems

A streamline upwind finite element method using 6-node triangular element is presented. The method is applied to the convection term of the governing transport equation directly along local streamlines. Several convective-diffusion examples are used to evaluate efficiency of the method. Results show that the method is monotonic and does not produce any oscillation. In addition, an adaptive meshing technique is combined with the method to further increase accuracy of the solution, and at the same time, to minimize computational time and computer memory requirement.

Dynamics of Ice Jam Formation and Release

The numerical model DynaRICE and its application to ice jam formation and release is presented. The model is a two-dimensional coupled flow and ice dynamic model. The ice dynamic component, which includes both the internal ice resistance and boundary friction on ice motion, uses a Lagrangian SPH method. The hydrodynamic component of the model uses a streamline upwind finite element method, which is capable of simulating trans-critical flow conditions. The model is validated with field observed ice jam data. The phenomena of ice jam formation and release dynamics are examined using the validated model.

Large Eddy Simulation of Homogeneous Isotropic Turbulent Flow Using the Finite Element Method

This paper presents results of validation study of large eddy simulation (LES) that is applied to homogeneous isotropic turbulence in order to assess its spectral accuracy. The LES is performed by using a streamline-upwind finite element method with second order accuracy both in time and space and the results are compared with those from direct numerical simulation (DNS) based on the spectral method. The validation tests are done by using Standard Smagorinsky Model (SSM) and Dynamic Smagorinsky Model (DSM), and include following two cases: a low Reynolds number case and a higher Reynolds number case. In the former case, the Reynolds number is low enough that the computational grid is capable of resolving all the turbulence scales. In this case our interest is in whether any effects of the subgrid scale (SGS) model should appropriately be dampened out. In the latter case, a relatively large Reynolds number is selected where effects of turbulent eddies that are not resolved by the computational grid should be properly taken into account by the SGS model. It is confirmed that DSM performs better than SSM for both cases and it gives good agreement with DNS results in terms of both spatial spectra and decay of the turbulence statistics. Visualization of the computed flow fields by the DSM also reveals existence of distinct, coherent and tube-like vortical structures similar to those found in instantaneous flow fields computed by the DNS.

Streamline upwind finite element method for conjugate heat transfer problems

This paper presents a combined finite element method for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow. The streamline upwind finite element method is used for the analysis of thermal viscous flow in the fluid region, whereas the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the proposed method is to consistently couple heat transfer along the fluid-solid interface. Three test cases, i.e. conjugate Couette flow problem in parallel plate channel, counter-flow in heat exchanger, and conjugate natural convection in a square cavity with a conducting wall, are selected to evaluate the efficiency of the present method.

Simulation of Melt Spinning of Nylon-6 Using the Finite Element Method

The properties of polymer melts are different from those of monomeric materials because polymer materials have crystalline and amorphous regions. In addition, polymer melts exhibit elasticity as well as viscosity. Therefore, the viscoelasticity, crystallinity and temperature of polymer melts must be considered for an accurate simulation of the melt spinning process for crystalline polymers. In this study, we simulated the melt spinning process of Nylon-6 by using the streamline-upwinding finite element method. The non-isothermal Phan-Thien Tanner model proposed by Sugeng and Phan-Thien was employed as a constitutive equation. We investigated the distribution of temperature and crystallinity on the free surface of the filament, and the filament diameter.The calculations were nearly independent of gravity. The primary normal stress increases and the filament diameter decreases with an increase of take-up speed. The filament diameter obtained by the non-isothermal flow simulation is smaller than that for the isothermal case, and the filament diameter depends on the crystallinity. The filament shape for a purely viscous fluid is the same as that for a viscoelastic one.

Non-isothermal Simulation of an Annular Extrudate Swell

The flow phenomena of polymer melts that are important in polymer processing depend on properties such as viscosity, relaxation time and temperature distribution. In this study, we focused on the annular extrudate swell problem that can be seen in pipe molding and hollow fiber spinning. The effects of gap width and wall temperature of an annular die on the swelling ratios of annular extrudates have been investigated by a non-isothermal viscoelastic flow simulation using a streamline-upwinding finite element method. The non-isothermal Phan-Thien Tanner model proposed by Sugeng and Phan-Thien (J. Rheol., 31, 37 (1987)) was employed as a constitutive equation.The calculated results for the outer free surface are in agreement with experimental data near the die outlet in the low shear rate region. As the mean velocity in the die increases, both the outer diameter swelling ratio χfo and the thickness swelling ratio χT increase. In the case of a constant outer diameter, χfo and χT increase with an increase of the diameter ratio κ, which is the inner die diameter divided by the outer die diameter. As the inner die wall temperature rises, higher χfo and lower χT are observed.

修正Ｇｉｅｓｅｋｕｓモデルによる紡糸過程の２層ダイスウェルシミュレーション

The main aim of this paper is to evaluate the applicability of a Modified Giesekus model to numerical simulation of double-layer flow in the spinning process. Numerical simulations of doublelayer flow from tube-in-orifice spinnerets have been carried out using a Modified Giesekus model. The streamline-upwinding finite element method with 4×4 sub-elements on stress components and over-relaxation method for equation of motion were used. In addition, the extrudate swell and interface shape have been experimentally observed for PVP (poly (vinylpyrrolidone)) aq./water system and comparisons between the numerical and the experimental results were made. It was found through both numerical predictions and experiments that extrudate swell shape is strongly dependent on the location of the center tube edge in a tube-in-orifice spinneret. Furthermore, the numerical and the experimental results are in good agreement for spinnerets with flush and projected center-tube. However, deviations have been found for the spinnerets with recessed center-tube. In addition, it was found that the Modified Giesekus model's prediction gives smaller swell compared to the original Giesekus one due to rapid stress relaxation.

High Weissenberg Number Simulation of Die Swell for Differential Type Viscoelastic Model by the Streamline-Upwind Finite Element Method

In order to predict the die swell seen in the actual polymer processing, the planar, the capillary and the annular die swell simulations have been performed by the streamline‐upwind finite element method with the subelements for stress components, which was shown effective to calculate up to high Weissenberg number (We) for the entry flow simulation in an earlier study. The calculation using the Giesekus model, which is the differential type viscoelastic model, was found feasible over hundreds of We in the planar and the capillary die swell simulations as long as the primary normal stress difference was not so large. The shape of free surface at high We under the condition of no gravitation once showed the maximum swell and became an equilibrium one after shrinking back a little. This tendency became remarkable for the model with larger We and larger primary normal stress difference. Through the examination of the velocity profile, it was found that the velocity near the free surface was accelerated durin...

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.

A monotone streamline upwind finite element method for convection-dominated flows

A new streamline upwind approximation for treating advection-dominatcd transport is presented. The proposed method is quite simple to implement with existing finite element methods. For this work, the method is used in a two-dimensional finite element computer program. The new method is applied to several test cases that have been presented in previous articles to evaluate the stability and accuracy of proposed methods for treating advection-dominatcd flows. The results demonstrate that the new method is able to predict the test cases with a significant increase in accuracy compared to previous techniques. In addition, these results demonstrate conclusively that the method does not exhibit the non-physical spatial oscillations that have plagued previous methods.