Two-dimensional Finite Volume Model Research Articles

Reduced finite-volume model for the fast numerical calculation of the fluid flow in the melt pool in laser beam welding

In this paper we propose a reduced two-dimensional finite-volume model for the fast calculation of the melt flow. This model was used to determine the influence of the welding speed, viscosity in the melt and vapour flow inside of the keyhole on the fluid flow field, the temperature distribution, and the resulting weld-pool geometry for laser beam welding of aluminium. The reduced computational time resulting from this approach allows the fast qualitative investigation of different aspects of the melt flow over a wide range of parameters. It was found that the effect of viscosity within the melt is more pronounced for lower welding speeds whereas the effect of friction at the keyhole walls is more pronounced for higher welding speeds. The weld-pool geometry mainly depends on the welding speed.

Numerical Simulation of Flood Inundation in a Small-Scale Coastal Urban Area Due to Intense Rainfall and Poor Inner Drainage

: This study presents the numerical simulation and analysis of the characteristics of the flood inundation in a small-scale coastal urban area due to the intense rainfall and poor inner drainage from the tidal level rise occurring during a typhoon. The employed numerical model is a two-dimensional finite volume model with a well-balanced HLLC (Harten–Lax–Van Leer contact) scheme. The target area is a coastal urban area downstream of the Gohyun river; which is located in Geoje City of Kyungsangnam Province, Korea. This area was significantly damaged by flood inundation due to the heavy rainfall and significant increase in the tidal level during Typhoon “Maemi”, which occurred in September 2003. The numerical model used in this study is verified using the flood inundation traces observed in the selected urban area. Moreover; the characteristics of the flood inundation based on the change in the river inflow due to the increase or decrease in the intensity of the possible heavy rainfall that may occur in the future are simulated and analyzed.

Coupled Numerical Approach for Automotive Battery Pack Lifetime Estimates With Thermal Management

This study combined a simple two-dimensional (2D) finite volume model (Kim model), which employs Ohm's law along with charge conservation over the electrodes and Butler–Volmer charge transfer kinetics for prismatic battery cells coupled with the single particle model (SPM) in order to model the thermal state of automotive battery packs. The objective here was to determine the effects of liquid cooling applied to the packs under standard driving cycles. A model developed by Kim provided a means for determining a nonuniform current distribution over the surface of the current collectors. The Kim model is based on the application of Ohm's law over a conducting medium, with empirical source terms representing current flowing into or out of an adjacent electrode layer. Here, a modeling advance is presented where empirical source terms in the Kim model were replaced with ones based on the chemistry and physics occurring inside the battery. As such, fundamental battery function was imparted to the model by integrating the SPM into the 2D finite volume Kim model. The 2D procedure described above was carried out on electrode sheets at different positions inside the cell, and determined thermal generation values that were mapped volumetrically into a heat transfer simulation, which, in turn, updated the electrochemical simulation. Capacity fade kinetics were determined by fitting experimental data to simulated results. With time-temperature profiles produced as described above for different pack cooling levels and varying degrees of cell degradation, a basic SPM simulation was then used with thermal overlays to estimate automotive cell life under various driving scenarios and various cooling levels. With these simulations, scenarios representing different thermal management regimes along with driving behavior were able to show the combined impact on automotive battery pack lifetimes.

A CFD Model for Prediction of the Role of Biomass Growth and Decay on the Aerobic Biodegradation of BTEX Fate and Transport in an Unconfined Aquifer System

This paper investigates the importance of considering biomass growth and decay for predicting a field scale microbial degradation of BTEX plume in an unconfined aquifer system in the Pump station area of Tehran oil refinery (TOR), Iran. A two-dimensional finite volume model has been presented to predict multi-species reactive transport incorporating physical, chemical and biological processes in the saturated zone of the aquifer. A multi-purpose commercial software called PHOENICS was modified to solve model equations. A complex Monod approach considering microbial growth and decay employed to describe the biodegradation of BTEX. The results of Monod approach was compared to those results obtained by three kinetics models including zero-order, first-order and Michaelis-Menten expressions that do not support biomass growth and decay. Monod approach predicted a further spreading of the plume. Other kinitics models underestimated the concentrations of BTEX plume, due to neglecting a high bacterial population and increased uptake rate. They are not appropriate to simulate tansport of biodegradable BTEX in the study aquifer. The model predictions agree well with the field measurements with an average error of 5%; describing that the Monod kinetics was well able to simulate the behaviour of the BTEX plume due to supporting bacterial population and considering oxygen as the electron acceptor.

Pre-monsoon hydrodynamic modeling of Goa coast, West coast of India

Attempt has been made to characterize the hydrodynamic regime around the coastal waters of Goa for a pre-monsoon season, using MOHID, a two-dimensional finite volume model. The numerical model was forced with tides at open boundaries and calibrated using measured water levels and currents, during pre-monsoon season. The modeled water levels and currents were compared with field observations and found to be satisfactory, with correlation of 0.97 for water levels, 0.79 for zonal currents, and 0.84 for meridional currents. The ratio of diurnal (O1, K1) and semidiurnal (M2, S2) constituents was 0.63, suggesting that tides in this region are mixed, mainly semidiurnal in nature. The variation in amplitude of tidal constituents from the open boundary to the mouth and upstream of the Mandovi and Zuari estuaries has been modeled and compared with previous field studies and found to be satisfactory. The details of numerical scheme, methodology, and results are discussed in this paper.

A study on simulation of flood inundation in a coastal urban area using a two-dimensional well-balanced finite volume model

In this study, the simulation and analysis of the inundation in a coastal urban area according to the storm surge height are carried out using a two-dimensional finite-volume model with a well-balanced scheme. The target coastal urban area considered in this study is a part of the new town of Changwon city, Gyeongnam province, South Korea; this area was extremely damaged by the storm surge generated during the period of Typhoon Maemi in September 2003. For the purpose of the verification of the numerical model applied in this study, the simulated results are compared and analyzed with the temporal storm surge heights observed at the tide station in Masan Bay and inundation traces in an urban area. Moreover, in order to investigate the influence of super-typhoons possible in the future, the results simulated with the storm surge heights, which were 1.25 and 1.5 times higher than those observed during the period of Typhoon Maemi, are compared and analyzed.

An efficient unstructured MUSCL scheme for solving the 2D shallow water equations

The aim of this paper is to present a novel monotone upstream scheme for conservation law (MUSCL) on unstructured grids. The novel edge-based MUSCL scheme is devised to construct the required values at the midpoint of cell edges in a more straightforward and effective way compared to other conventional approaches, by making better use of the geometrical property of the triangular grids. The scheme is incorporated into a two-dimensional (2D) cell-centered Godunov-type finite volume model as proposed in Hou et al. (2013a,c) to solve the shallow water equations (SWEs). The MUSCL scheme renders the model to preserve the well-balanced property and achieve high accuracy and efficiency for shallow flow simulations over uneven terrains. Furthermore, the scheme is directly applicable to all triangular grids. Application to several numerical experiments verifies the efficiency and robustness of the current new MUSCL scheme.

Multislope MUSCL method applied to solve shallow water equations

Based on a classical multislope MUSCL (monotone upstream scheme for conservation law) method, this paper addresses a new multislope MUSCL method which is used to extrapolate the values of flow variables at the midpoints of cell edges. The main merit of the new method is its more straightforward implementation than that of the classical one. The new method is incorporated into a two-dimensional unstructured cell-centered Godunov-type finite volume model to simulate shallow water flows. The performance of the model with the new multislope MUSCL method is demonstrated by simulating three test cases including both theoretical and practical ones. It is verified that the new method is more efficient than the classical one and is able to produce slightly better or similar numerical results.

Numerical Simulation of Two-Dimensional Unsaturated Flow from a Trickle Irrigation Source Using the Finite-Volume Method

AbstractA numerical two-dimensional finite-volume model is developed to predict the moisture-based form of the Richard’s equation that describes the transient flow of water through homogeneous and ...

Short-time performance of composite-medium line-source model for predicting responses of ground heat exchangers with single U-shaped tube

A composite-medium line-source model has been recently developed for modeling short-time thermal processes of borehole ground heat exchangers. The composite-medium line-source model is attractive for applications where the short-term or high-frequency responses of borehole ground heat exchangers are important. In this paper, the short-time performance of this analytical model is examined in depth by comparing it with a two-dimensional finite volume model. The numerical model can address the heat capacity of circulating water by using a novel time-varying boundary condition on the inner walls of the U-shaped tube, in addition to the heat capacities of U-shaped tube and grouting material. Both the numerical and the analytical composite-medium models are validated using an independent sandbox experiment. Comparisons between the two models are also made for different parameters, including heating rate, the spacing of the U-tube legs, thermal properties, and borehole radius. Overall, the composite-medium line-source model gives the virtually same results as the numerical model except for the first several minutes: the analytical solution overestimates temperature responses during the first 3 min, which is caused by the line-source assumption ignoring the heat capacities of the fluid and the U-shaped pipe.

Closure to “Two-dimensional depth-averaged finite volume model for unsteady turbulent flow”

"Closure to “Two-dimensional depth-averaged finite volume model for unsteady turbulent flow”." Journal of Hydraulic Research, 52(1), pp. 150–151

Two-dimensional depth-averaged finite volume model for unsteady turbulent flows

By CHUNSHUI YU and JENNIFER DUAN, J. Hydraulic Res. 50(6), 2012, 599–611The development of a state of the art two-dimensional (2D) depth-averaged flow model coupled with a k–ϵ turbulence model such...

A Well-Balanced Numerical Model for the Simulation of Long Waves over Complex Domains

This paper presents a well-balanced two-dimensional (2D) finite volume model to simulate the propagation, runup and rundown of long wave. Non-staggered grid is adopted to discretize the governing equation and the intercell flux is computed using a central upwind scheme, which is a Riemann-problem-solver-free method for hyperbolic conservation laws. The nonnegative reconstruction method for water depth is implemented in the present model to treat the appearance of wet/dry fronts, and the friction term is solved by a semi-implicit scheme to ensure the stability of the model. The Euler method is applied to update flow variable to the new time level. The model is verified against two experimental cases and good agreements are observed between numerical results and observed data.

Self-Adaptive Kinematic-Dynamic Model for Overland Flow

AbstractThe authors developed an innovative two-dimensional finite-volume model for overland flow, which is capable of simultaneously applying the kinematic wave approximation and the full Saint-Venant (dynamic) equations to different regions of the modeled domain. A locally based criterion is employed to determine the applicability limits for the kinematic approximation. The model assesses the flow and topography on a cell-by-cell basis at each time step over an unstructured, triangular grid and determines the appropriate solution method for each individual cell. Several case studies are shown that illustrate the adaptive kinematic-dynamic model’s flexibility and robustness. The effects of the user-defined limit for the kinematic wave approximation and the abrupt switch from one solver to another are explored for the adaptive kinematic-dynamic model.

Numerical simulation of shallow-water flooding using a two-dimensional finite volume model

A 2-D Finite Volume Model (FVM) is developed for shallow water flows over a complex topography with wetting and drying processes. The numerical fluxes are computed using the Harten, Lax, and van Leer (HLL) approximate Riemann solver. Second-order accuracy is achieved by employing the MUSCL reconstruction method with a slope limiter in space and an explicit two-stage Runge-Kutta method for time integration. A simple and efficient method is introduced to deal with the wetting and drying processes without any correction of the numerical flux term or the source term. In this new method, a switch of alternative schemes is used to compute the water depths at the cell interface to obtain the numerical flux. The model is verified against benchmark tests with analytical solutions and laboratory experimental data. The numerical results show that the model can simulate different types of flood waves from the ideal flood wave to cases over complex terrains. The satisfactory performance indicates an extensive application prospect of the present model in view of its simplicity and effectiveness.

Sample dispersion in isotachophoresis with Poiseuille counterflow

A particular mode of isotachophoresis (ITP) employs a pressure-driven flow opposite to the sample electromigration direction in order to anchor a sample zone at a specific position along a channel or capillary. We investigate this situation using a two-dimensional finite-volume model based on the Nernst-Planck equation. The imposed Poiseuille flow profile leads to a significant dispersion of the sample zone. This effect is detrimental for the resolution in analytical applications of ITP. We investigate the impact of convective dispersion, characterized by the area-averaged width of a sample zone, for various values of the sample Péclet-number, as well as the relative mobilities of the sample and the adjacent electrolytes. A one-dimensional model for the area-averaged concentrations based on a Taylor-Aris-type effective axial diffusivity is shown to yield good agreement with the finite-volume calculations. This justifies the use of such simple models and opens the door for the rapid simulation of ITP protocols with Poiseuille counterflow.

An Assessment of Factors Affecting Reactive Transport of Biodegradable BTEX in an Unconfined Aquifer System, Tehran Oil Refinery, Iran

Risk-based assessment methods are commonly used at the contaminated sites by hydrocarbon pollutants. This paper presents the results of a two-dimensional finite volume model of reactive transport of biodegradable BTEX which have been developed for the saturated zone of an unconfined aquifer in the Pump station area of Tehran oil refinery, Iran. The model governing equations were numerically solved by modification of a general commercial software called PHOENICS. To reduce costs in general, many input parameters of a model are often approximated based on the used values in the contaminated sites with same conditions. It was not fully recognised the effect of errors in these inputs on modelling outputs. Thus, a sensitivity analysis was carried out to determine the influence of parameters variability on the results of model. For this analysis, the sensitivity of the model to changes in the dispersivity, distribution coefficient, parameters of Monod, Michaelis-Menten, first- and zero- order kinetics modes on the BTEX contaminant plume were examined by performing several simulations. It was found that the model is sensitive to changes in dispersivity and parameters of Michaelis-Menten, first- and zero- order kinetics model. On the other hand, the predictions for plumes assuming Monod kinetics are similar, even if different values for parameterization are chosen. The reason for this insensibility is that degradation is not limited by microbial kinetics in the simulation, but by dispersive mixing. Quantifying the effect of changes in model input parameters on the modelling results is essential when it is desired to recognise which model parameters are more vital on the fate and transport of reactive pollutants. Furthermore, this process can provide an insight into understanding pollutant transportation mechanisms.

해안도시지역 홍수범람모의에 관한 연구: 경상남도 거제시 고현천 적용사례

In this study, the simulations and analyses of flood flow due to a river inundation in a coastal urban area are carried out using a two-dimensional finite volume model with well-balanced HLLC scheme. The target area is a coastal urban area around Gohyun river which is located at Geoje city in Kyungnam province and was extremely damaged due to the heavy rainfall during the period of the typhoon Maemi in September 2003. For the purpose of the verification of the numerical model applied in this study, the simulated results are compared and analyzed with the inundation traces. In addition, the flood flow in an urban area is simulated and analyzed according to the scenarios of inflow variation due to the increase and decrease of the intensity of the heavy rainfall, which.

Two-dimensional depth-averaged finite volume model for unsteady turbulent flow

A two-dimensional (2D) depth-averaged model is developed for simulating unsteady turbulent shallow-water flows with dry–wet fronts (e.g. dam-break flow). The model is based on 2D depth-averaged Reynolds-averaged Navier stokes equations coupled with the k−ϵ turbulence model. The high-resolution MUSCL scheme (monotone upstream-centred schemes for conservation laws) is implemented to minimize numerical diffusions. A novel augmented Harten–Lax–van Leer-contact Riemann solver is used to solve the governing equations simultaneously. A body-fitted mesh is generated by using the Cartesian cut-cell method to accommodate irregular boundaries. The model is tested against two laboratory experiments to examine whether or not turbulence model is essential for simulating unsteady turbulent flow. The results show that the addition of the k−ϵ turbulence model significantly improves the modelling results at places of strong turbulence activities. To further improve the results, a more accurate turbulence model for unsteady flow and dispersion terms in the momentum equations is needed.

A high-resolution shallow water model using unstructured quadrilateral grids

A two-dimensional cell-centred finite volume model for quadrilateral grids is presented. The solution methodology of the depth-averaged shallow water equations is based upon a Godunov-type upwind finite volume formulation, whereby the inviscid fluxes of the system of equations are obtained using the HLL Riemann solver. A simple yet precise analytical expression is presented to compute hydrostatic flux through an interface of a quadrilateral cell in order to achieve exact balance between flux gradient and bed slope source terms under still water condition. A multidimensional gradient reconstruction procedure and a continuously differentiable multidimensional slope limiter based on a wide computational stencil are proposed to maintain second-order spatial accuracy. The proposed second-order scheme is shown to be more accurate even when distorted grids are used and is therefore more suitable for practical applications. The presented model is verified and validated by solving a wide variety of test cases having analytical solutions and laboratory measurements.