Finite Volume Method Simulation Research Articles

Finite Element and Finite Volume Method for Simulation of Free Surface Flows: Application to Spillways

Finite Element and Finite Volume Method for Simulation of Free Surface Flows: Application to Spillways

A theoretical and experimental investigation of spatial distribution of radon in a typical ventilated room

The aim of this work is to studying indoor radon distribution using the Finite Volume Method (FVM). This paper focuses on effects of exhalation from different sources (wall, floor and ceiling) and the ventilation profile on distribution the concentrations of radon indoor. The rate of radon exhalation and ventilation were measured and are used as input in FVM simulation. It has been found that the radon concentration is distributed in non homogeneous way in the room. The radon concentration is much larger near floor, and decreases in the middle of the room. The experimental validation was performed by measuring radon concentration at different locations in room using active and passive techniques. We notice that the results of simulation and experimental are in agreement. The annual effective dose of radon in the model room has been also investigated.

On the Treatment of Field Quantities and Elemental Continuity in FEM Solutions.

As the finite element method (FEM) and the finite volume method (FVM), both traditional and high-order variants, continue their proliferation into various applied engineering disciplines, it is important that the visualization techniques and corresponding data analysis tools that act on the results produced by these methods faithfully represent the underlying data. To state this in another way: the interpretation of data generated by simulation needs to be consistent with the numerical schemes that underpin the specific solver technology. As the verifiable visualization literature has demonstrated: visual artifacts produced by the introduction of either explicit or implicit data transformations, such as data resampling, can sometimes distort or even obfuscate key scientific features in the data. In this paper, we focus on the handling of elemental continuity, which is often only continuous or piecewise discontinuous, when visualizing primary or derived fields from FEM or FVM simulations. We demonstrate that traditional data handling and visualization of these fields introduce visual errors. In addition, we show how the use of the recently proposed line-SIAC filter provides a way of handling elemental continuity issues in an accuracy-conserving manner with the added benefit of casting the data in a smooth context even if the representation is element discontinuous.

Lattice Boltzmann Method of Different BGA Orientations on I-Type Dispensing Method.

This paper studies the three dimensional (3D) simulation of fluid flows through the ball grid array (BGA) to replicate the real underfill encapsulation process. The effect of different solder bump arrangements of BGA on the flow front, pressure and velocity of the fluid is investigated. The flow front, pressure and velocity for different time intervals are determined and analyzed for potential problems relating to solder bump damage. The simulation results from Lattice Boltzmann Method (LBM) code will be validated with experimental findings as well as the conventional Finite Volume Method (FVM) code to ensure highly accurate simulation setup. Based on the findings, good agreement can be seen between LBM and FVM simulations as well as the experimental observations. It was shown that only LBM is capable of capturing the micro-voids formation. This study also shows an increasing trend in fluid filling time for BGA with perimeter, middle empty and full orientations. The perimeter orientation has a higher pressure fluid at the middle region of BGA surface compared to middle empty and full orientation. This research would shed new light for a highly accurate simulation of encapsulation process using LBM and help to further increase the reliability of the package produced.

Direct FVM Simulation for Sound Propagation in an Ideal Wedge

The sound propagation in a wedge-shaped waveguide with perfectly reflecting boundaries is one of the few range-dependent problems with an analytical solution. This provides a benchmark for the theoretical and computational studies on the simulation of ocean acoustic applications. We present a direct finite volume method (FVM) simulation for the ideal wedge problem, and both time and frequency domain results are analyzed. We also study the broadband problem with large-scale parallel simulations. The results presented in this paper validate the accuracy of the numerical techniques and show that the direct FVM simulation could be applied to large-scale complex acoustic applications with a high performance computing platform.

Air damping as design feature in lateral oscillators

The damping of an oscillator is, next to the effective mass and the stiffness, one of the key parameters that determine its frequency response as well as its noise. Since there are numerous different applications for oscillating microstructures, there are also numerous requirements for the shape of the respective resonance peak. While fabricating the right mass and stiffness to obtain a desired resonance frequency is, in general, a basic task, designing a micro-oscillator featuring an intended damping is not trivial. We present a way of utilizing the surrounding air to adjust the passive damping of a laterally oscillating micromechanical system. This is shown to hold in a relatively wide range by comparing analytical models and finite volume method simulations with measurements of a number of micro-electro-mechanical test structures with optical readout.

Parallel Finite Volume Method Simulation of Three-Dimensional Fluid Flow and Convective Heat Transfer for Viscoplastic Non-Newtonian Fluids

Three-dimensional fluid mechanics and heat transfer for viscoplastic flows are described by finite volume method, FVM. The open multi-processing approach has been implemented to parallelize the numerical code. Results for the elapsed times, speed-ups and efficiencies are presented. The code was used to describe the natural convection (Ra = 104; 106) and the lid-driven cavity (Re = 100; 1000) processes with Bingham, Casson and Herschel–Bulkley fluids (Bn = 0.01; 1.0). Results describing isotherms, velocity distributions and streamtraces, as a function of Ra, Re, Pr and Bn numbers are shown. The grid size analysis shows that different sizes are required to obtain precise results for Nusselt number and friction factor.

Efficient simulation of three-dimensional marine controlled-source electromagnetic response in anisotropic formation by means of coupled potential finite volume method

A coupled potential finite volume method for simulation of three-dimensional marine controlled-source electromagnetic (CSEM) response in anisotropic formation is developed. To circumvent ill-conditioning and convergence problems, Maxwell's equations are reformulated into coupled scalar-vector potentials with Coulomb gauge and its complement by applying a Helmholtz decomposition to the electric field. Yee's staggered girds, finite volume averaging and interpolation techniques are used to make the Helmholtz equations discrete. The resulting sparse and complex linear system in large-scale models is solved by a direct solver PARDISO. In order to improve the accuracy of the near field results without significantly reducing the computational efficiency, a method using difference fields is proposed to reduce the source singularity effect of anisotropic formation. The anisotropic modeling examples show that marine CSEM response is predominantly sensitive to reservoir vertical resistivity, not to reservoir horizontal resistivity, provided that the reservoir are thin and high-resistive; but the marine CSEM response is sensitive to both horizontal and vertical resistivity of the overburden on top of the reservoir.

Enhancement of upward thermal dissipation in a 16-Chip LED package using ceramic barrier ribs

To enhance the upward thermal dissipation characteristics in a 16-chip light emitting diode (LED) package, ceramic barrier ribs were introduced between the LED chips. A FLIR T-250 IR microscopy camera was used to measure the top surface temperature of the package, which decreased from 116°C to 112°C at 2.5W operation because of the ceramic barrier ribs. A finite volume method simulation was conducted to estimate the temperature distribution inside the package, including the junction temperature. This simulation showed that the junction temperature decreased from 119°C to 114°C because of the barrier ribs. This result occurred because the ceramic barrier ribs provided a more effective upward heat dissipation path for the mid-chips, which contributed to the decrease in the junction temperature.

A multi-resolution multiscale finite volume method for simulation of fluid flows in heterogeneous porous media

This paper presents an extension of the multiscale finite volume (MsFV) method to multi-resolution coarse grid solvers for single phase incompressible flows. To achieve this, a grid one level coarser than the coarse grids used in the MsFV method is constructed and the local problems are redefined to compute the basis and correction functions associated with this new grid. To construct the coarse-scale pressure equations, the coarse-scale transmissibility coefficients are calculated using a new multi-point flux approximation (MPFA) method. The estimated coarse-scale pressures are utilized to compute the multiscale pressure solution. Finally a reconstruction step is performed to produce a conservative velocity field which is used to solve the transport equations. The computational cost of the proposed method is compared with that of the MsFV method and the relevant time complexity formulas are given. Several two-dimensional test cases with permeability fields ranging from two-scale to multi-scale problems are solved. The performance of the proposed method in handling problems with shale layers or discrete fractures is assessed. Also, a number of layers from the tenth SPE comparative study problem are used to examine general abilities of the method when facing realistic reservoir problems. The results are compared with fine-scale reference solutions to assess the accuracy of the proposed method.

Estimation of heat dissipation through the interchip structure for a multichip light-emitting diode package via simulation

The heat dissipation through interchip structures was investigated by introducing 4-partition and 16-partition ceramic interchip structures for a 16-chip light-emitting diode (LED) package. Using the finite volume method simulation with ICEPAK V13.0, the temperature distribution inside the LED package and the junction temperature were estimated, from which the effect of the interchip structures on the heat dissipation characteristics of the LED package was investigated. The results showed that the ceramic interchip structures provided a more effective upward heat dissipation path for the LED package and contributed to a 23°C decrease in the junction temperature for the 4-partition interchip structure and a 51°C decrease for the 16-partition interchip structure at the 16 W operation.

Numerical Simulation of the Formation of Granular Shock Wave Over Cylindrical Obstacle

AbstractA two dimensional (2‐D) stream of granular flow with zero initial granular temperature passing over a cylindrical obstacle is simulated by means of both molecular dynamics (MD) simulation and finite volume method (FVM). In experiments, a bow‐shaped shock wave with higher area fraction forms in front of the obstacle that was reproduced in our simulations. Due to the different circumstances to which particles are subjected, the granular flow is divided in two zones. One is undisturbed where quantities, such as space fraction (volume fraction for 3‐D and area fraction for 2‐D geometries), velocity and granular temperature are uniformly distributed and the other is called the shock wave zone. In this region, the values of the space fraction increases and the velocity of particles changes. From the MD simulation, it is found that the area fraction of the shock wave depends on surface roughness, coefficient of restitution (COR) of particles, the obstacle diameter as well as velocity of the granular stream, and a triangular region forms with almost zero velocity, and granular temperature forms in front of the cylindrical obstacle. The bigger is the size of the obstacle, the more stable this region is. In FVM simulations solid phase velocity and area fraction distributions similar to the MD simulation results are obtained for proper parameters.

Direct numerical simulation of pore-scale reactive transport: applications to wettability alteration during two-phase flow

We present a finite element – finite volume simulation method for modelling fluid flow and solute transport accompanied by chemical reactions in experimentally obtained 3D pore geometries. The advantage of the proposed methodology with respect to other pore-scale modelling approaches is that no simplifications regarding the geometry of the porous space are required and no approximations to the flow equations are introduced. We apply this method in a proof-of-concept study of a digitised Fontainebleau sandstone sample. We use the calculated velocity profile with the finite volume procedure to simulate pore-scale transport and diffusion of the adsorbing solute. We also demonstrate how analysis of the pore geometry can be used to identify the locations of oil during the two-phase flow and couple this with the reactive transport modeling to show how this procedure can be used to estimate the potential of the enhanced oil recovery techniques.

Body Fitted Grids Based FVM Simulation of Aluminum Extrusion Process

A body fitted based finite volume method (FVM) model of aluminum extrusion processes was established in this paper. The basic theories and rigid-plastic flow theories of this model were researched and built. Body fitted grids were used to match complex geometric boundaries and local refinement of grids was also realized. Plastic shear friction model was applied on body fitted grids. A typical then walled profile extrusion process was simulated using the program developed in this paper. The simulation results were also compared with that simulated by FEM software Deform in the same process, material and die conditions. The feasibility and efficiency of the mathematic model built in this paper was demonstrated by the simulation results and the comparison.

FVM Simulation of the Effect of Preventing Ring Structure on Continuous Extrusion Process

Continuous extrusion is an advanced process for manufacturing copper bus-bar while preventing ring is an important factor affecting forming. Due to the severe plastic deformation, FE simulation of continuous extrusion extending deforming is inaccurate and inefficient because of frequent remesh. Based on finite volume method (FVM) which can avoid re-mesh effectively, this paper simulates continuous extrusion forming, and analyzes the effect of different preventing ring structure on metal flowing velocity. The results show that: preventing ring with the curve transitional surface is beneficial to metal uniform flowing than that with the plane transitional surface; As radius of preventing ring increases, the metal flow rate of the sides is faster than the middle part; As opening width of preventing ring increases, the dead metal zones become smaller in the middle area.

Efficient flow and transport simulations in reconstructed 3D pore geometries

Upscaling pore-scale processes into macroscopic quantities such as hydrodynamic dispersion is still not a straightforward matter for porous media with complex pore space geometries. Recently it has become possible to obtain very realistic 3D geometries for the pore system of real rocks using either numerical reconstruction or micro-CT measurements. In this work, we present a finite element–finite volume simulation method for modeling single-phase fluid flow and solute transport in experimentally obtained 3D pore geometries. Algebraic multigrid techniques and parallelization allow us to solve the Stokes and advection–diffusion equations on large meshes with several millions of elements. We apply this method in a proof-of-concept study of a digitized Fontainebleau sandstone sample. We use the calculated velocity to simulate pore-scale solute transport and diffusion. From this, we are able to calculate the a priori emergent macroscopic hydrodynamic dispersion coefficient of the porous medium for a given molecular diffusion D m of the solute species. By performing this calculation at a range of flow rates, we can correctly predict all of the observed flow regimes from diffusion dominated to convection dominated.

Optimization of concrete hollow brick using hybrid genetic algorithm combining with artificial neural networks

A structure optimization of concrete hollow brick with four rectangle enclosures is carried out to minimize the equivalent thermal conductivity (ETC) in the constraint of variable shape and position parameters. During the optimization hybrid genetic algorithm (HGA) is developed combining with artificial neural networks (ANN). The modified Latin hypercube sampling (i.e. the maximum minimum distance criterion) is employed to make a robust decision. The ETC of the samples is computed using the finite volume method (FVM) on the basis of 3D multi-mode heat transfer simulation. It indicates that the well-trained ANN can accurately predict the ETC of the concrete hollow brick which matches very well with data obtained from the FVM simulation. The optimization obtains 21.69% improvement on the ETC for the given range of design parameters. The optimized concrete hollow brick owns the largest void volume fraction, the minimum rid and wall thickness, same width of the enclosure, and the optimum staggered arrangement with two same large enclosures and two same small enclosures, which is resulted by the multi-mode heat transfer characteristic of the concrete hollow brick. A novel method of the optimum concrete hollow is proposed to construct new concrete hollow brick with many rows of enclosures. Relative Staggered Ratio (RSR) is used to discuss the effect of the staggered form. By combining two or more rows of the optimized enclosures to one brick with the same size the efficiency to block heat transfer is evidently improved. It is concluded by the present work that the combination of ANN and HGA and the popularizing method are powerful to the optimization of the concrete hollow brick.

Finite Volume Simulation and Multi Parameters Optimization on Extrusion of Complex Aluminum Profile

In this paper, finite volume method (FVM) is adopted to simulate complex irregular aluminum profile extrusion process. The basic theory of FVM, the materials model, friction model, and a computer aided optimization (CAO) model based on orthographic experiments, artificial neural network (ANN) and genetic algorithm (GA) are presented. A complex aluminum profile extrusion is simulated and optimized. The results show FVM simulation is a good way for the description of material flow, and mesh distortion could be avoided effectively. Optimal values of multi parameters are also obtained. Experiment shows good fit among the simulation, optimization and the experimental results.

Finite volume method for simulation of viscoelastic flow through a expansion channel

A finite volume method for the numerical solution of viscoelastic flows is given. The flow of a differential Upper-Convected Maxwell (UCM) fluid through an abrupt expansion has been chosen as a prototype example. The conservation and constitutive equations are solved using the Finite Volume Method (FVM) in a staggered grid with an upwind scheme for the viscoelastic stresses and a hybrid scheme for the velocities. An enhanced-in-speed pressure-correction algorithm is used and a method for handling the source term in the momentum equations is employed. Improved accuracy is achieved by a special discretization of the boundary conditions. Stable solutions are obtained for higher Weissenberg number ( We), further extending the range of simulations with the FVM. Numerical results show the viscoelasticity of polymer solutions is the main factor influencing the sweep efficiency.

Finite volume method for simulation of extrusion processes

AbstractIn this paper, the development of a finite volume method for prediction of plastic flow of metals during cold and hot extrusion processes is described. The method solves the equations governing mass, momentum and heat balance in their integral form, using discretization elements of an arbitrary polyhedral shape. Comparisons of the numerical and experimental results show a very good agreement, implying that the proposed numerical method can be used as a useful tool in designing extrusion processes. Copyright © 2005 John Wiley & Sons, Ltd.