Explicit Finite Volume Method Research Articles

A cellular automaton – finite volume method for the simulation of dendritic and eutectic growth in binary alloys using an adaptive mesh refinement

A two-dimensional model to simulate the dendritic and eutectic growth in binary alloys is developed. A cellular automaton method is adopted to track the movement of the solid–liquid interface. The diffusion equation is solved in the solid and liquid phases by using an explicit finite volume method. The computational domain is divided into square cells that can be hierarchically refined or coarsened using an adaptive mesh based on the quadtree algorithm. Such a mesh refines the regions of the domain near the solid–liquid interface, where the highest concentration gradients are observed. In the regions where the lowest concentration gradients are observed the cells are coarsened. The originality of the work is in the novel, adaptive approach to the efficient and accurate solution of the posed multiscale problem. The model is verified and assessed by comparison with the analytical results of the Lipton–Glicksman–Kurz model for the steady growth of a dendrite tip and the Jackson–Hunt model for regular eutectic growth. Several examples of typical microstructures are simulated and the features of the method as well as further developments are discussed.

A priori analysis of multilevel finite volume approximation of 1D convective Cahn–Hilliard equation

In this work, we analyze four finite volume methods for the nonlinear convective Cahn–Hilliard equation with specified initial condition and periodic boundary conditions. The methods used are: implicit one-level, explicit one-level, implicit multilevel and explicit multilevel finite volume methods. The existence and uniqueness of solution, convergence and stability of the finite volume solutions are proved. We compute $$L_2$$ - error and rate of convergence for all methods. We then compare the multilevel methods with the one-level methods by means of stability and CPU time. It is shown that the multilevel finite volume method is faster than the one-level method.

An asymptotic-preserving method for a relaxation of the Navier–Stokes–Korteweg equations

The Navier–Stokes–Korteweg (NSK) equations are a classical diffuse-interface model for compressible two-phase flows. As direct numerical simulations based on the NSK system are quite expensive and in some cases even impossible, we consider a relaxation of the NSK system, for which robust numerical methods can be designed. However, time steps for explicit numerical schemes depend on the relaxation parameter and therefore numerical simulations in the relaxation limit are very inefficient. To overcome this restriction, we propose an implicit–explicit asymptotic-preserving finite volume method. We prove that the new scheme provides a consistent discretization of the NSK system in the relaxation limit and demonstrate that it is capable of accurately and efficiently computing numerical solutions of problems with realistic density ratios and small interfacial widths.

Compressibility effects on the flow past a rotating cylinder

In this paper, laminar flow past a rotating circular cylinder placed in a compressible uniform stream is investigated via a two-dimensional numerical simulation and the compressibility effects due to the combination of the free-stream and cylinder rotation on the flow pattern such as forming, shedding, and removing of vortices and also the lift and drag coefficients are studied. The numerical simulation of the flow is based on the discretization of convective fluxes of the unsteady Navier-Stokes equations by second-order Roe’s scheme and an explicit finite volume method. Because of the importance of the time dependent parameters in the solution, the second-order time accurate is applied by a dual time stepping approach. In order to validate the operation of a computer program, some results are compared with previous experimental and numerical data. The results of this study show that the effects due to flow compressibility such as normal shock wave caused the interesting variations on the flow around the cylinder even at a free-stream with a low Mach number. At incompressible flow around the rotating cylinder, increasing the speed ratio, α (ratio of the surface speed to free-stream velocity), causes the ongoing increase in the lift coefficient, but in compressible flow for each free-stream Mach number, increasing the speed ratio results in obtaining a limited lift coefficient (a maximum mean lift coefficient). In addition, results from the compressible flow indicate that by increasing the free-stream Mach number, the maximum mean lift coefficient is decreased, while the mean drag coefficient is increased. It is also found that by increasing the Reynolds number at low Mach numbers, the maximum mean lift coefficient and critical speed ratio are decreased and the mean drag coefficient and Strouhal number are increased. However at the higher Mach numbers, these parameters become independent of the Reynolds number.

Comparison of Three Different Parallel Computation Methods for a Two-Dimensional Dam-Break Model

Three parallel methods (OpenMP, MPI, and OpenACC) are evaluated for the computation of a two-dimensional dam-break model using the explicit finite volume method. A dam-break event in the Pangtoupao flood storage area in China is selected as a case study to demonstrate the key technologies for implementing parallel computation. The subsequent acceleration of the methods is also evaluated. The simulation results show that the OpenMP and MPI parallel methods achieve a speedup factor of 9.8× and 5.1×, respectively, on a 32-core computer, whereas the OpenACC parallel method achieves a speedup factor of 20.7× on NVIDIA Tesla K20c graphics card. The results show that if the memory required by the dam-break simulation does not exceed the memory capacity of a single computer, the OpenMP parallel method is a good choice. Moreover, if GPU acceleration is used, the acceleration of the OpenACC parallel method is the best. Finally, the MPI parallel method is suitable for a model that requires little data exchange and large-scale calculation. This study compares the efficiency and methodology of accelerating algorithms for a dam-break model and can also be used as a reference for selecting the best acceleration method for a similar hydrodynamic model.

A second-order Finite Volume Method for pipe flow with water column separation

A second-order explicit Finite Volume Method (FVM) based on Godunov-type schemes is presented and applied to water column separation (WCS) in pipelines. The treatment of two-phase fluid in the model is similar to the ideas of the classic discrete vapor cavity model (DVCM) based on method of characteristics (MOC). The challenge in using the FVM is how to capture vapor cavities and predict their growth and collapse. The FVM introduced here assumes the vaporous cavity is concentrated at the middle of control volume, and divides the local control volume into two equal halves, in order to calculate the vapor cavity volume. The proposed model is based on the exact Reimann solution of the coupled continuity and momentum equations, and second-order accuracy is achieved by means of data reconstruction based on slope limiter, an approach which prevents the development of spurious oscillations near in the vicinity of high gradients. Predictions of FVM-DVCM for transient pressures caused by WCS and rejoining are compared to published experimental data and to numerical results from the classic DVCM. Pressure results from FVM-DVCM show considerably better agreement with experimental data and significantly avoid unrealistic artificial spikiness with finer grids.

Numerical simulation of flow and bed morphology in the case of dam break floods with vegetation effect

The purpose of this study is to establish a depth-averaged 2-D hydrodynamic and sediment transport model for the dam-break flows with vegetation effect. The generalized shallow water equations are solved using an explicit finite volume method with unstructured quadtree rectangular grid, and in the hydrodynamic model, a Harten-Lax-Van Leer (HLL) approximate Riemann solver is used to calculate the intercell flux for capturing the dry-to-wet moving boundary. The sediment transport and bed variation equations in a coupled fashion are calculated by including the bed variation and the variable flow density in the flow continuity and momentum equations. The drag force of vegetation is modeled as the sink terms in the momentum equations. The developed model is tested against lab experiments of the dam-break flows over a fix bed and a movable bed in vegetated and non-vegetated channels. The results are compared with experimental data, and good agreement is obtained. It is shown that the reduced velocity under vegetated conditions leads to a decrease of the peak discharge and a rise of the water level of rivers and also an enhancement of the sediment deposition.

Numerical Study of Natural Convection Heat Transfer in a Horizontal Wavy Absorber Solar Collector Based on the Second Law Analysis

Literature about entropy generation analysis of a wavy enclosure is scare. In this paper. a FORTRAN cod using an explicit finite-volume method was provided for estimating the entropy production due to the natural convection heat transfer in a cosine wavy absorber solar collector. The volumetric entropy generation terms both the heat transfer term and the friction term were straightly calculated. The solution was conducted assuming the isothermal boundary conditions of the absorber and the cover of solar collector. the results were obtained for Rayleigh number from 100 to 100000. The simulation results were compared with a flat plate absorber. It was found that, with increasing of the cosine wave amplitude, the collector enclosure irreversibility decreases.

NUMERICAL INVESTIGATION OF THE UNSTART SUPPRESSION IN A SUPERSONIC AIR INTAKE

The starting behavior of a supersonic axisymmetric mixed compression air intake was numerically investigated. The code solves Reynolds-averaged Navier–Stokes equations using an explicit finite volume method in a structured grid by the Roe flux difference splitting scheme. Further, it uses the Baldwin–Lomax algebraic model to compute the turbulent viscosity coefficient. The correct method of surveying the intake starting problem and effects of several geometrical parameters such as: intake throat area, cowl lip roundness and spike surface curvature upstream of the throat on the starting and performance of the intake were studied. Results showed that correct combinations of the mentioned parameters can suppress the intake unstart problem and in addition can prevent the reduction of the intake efficiency.

Modeling of Breaching Due to Overtopping Flow and Waves Based on Coupled Flow and Sediment Transport

Breaching of earthen or sandy dams/dunes by overtopping flow and waves is a complicated process with strong, unsteady flow, high sediment transport, and rapid bed changes in which the interactions between flow and morphology should not be ignored. This study presents a depth-averaged two-dimensional (2D) coupled flow and sediment transport model to investigate the flow and breaching processes with and without waves. Bed change and variable flow density are included in the flow continuity and momentum equations to consider the impacts of sediment transport. The model adopts the non-equilibrium approach for total-load sediment transport and specifies different repose angles to handle non-cohesive embankment slope avalanching. The equations are solved using an explicit finite volume method on a rectangular grid with the improved Godunov-type central upwind scheme and the nonnegative reconstruction of the water depth method to handle mixed-regime flows near the breach. The model has been tested against two sets of experimental data which show that it well simulates the flow characteristics, bed changes, and sediment transport. It is then applied to analyze flow and morphologic changes by overtopping flow with and without waves. The simulated bed change and breach cross-section shape show a significant difference if waves are considered. Erosion by flow without waves mainly occurs at the breach and is dominated by vertical erosion at the initial stage followed by the lateral erosion. With waves, the flow overtops the entire length of the dune to cause faster erosion along the entire length. Erosion mainly takes place at the upper layer at the initial stage and gradually accelerates as the height of the dune reduces and flow discharge increases, which indicates the simulated results with waves shall be further verified by physical experimental evidence.

Mathematical model for flood routing in Jingjiang River and Dongting Lake network

The main stream of the Yangtze River, Dongting Lake, and the river network in the Jingjiang reach of the Yangtze River constitute a complex water system. This paper develops a one-dimensional (1-D) mathematical model for flood routing in the river network of the Jingjiang River and Dongting Lake using the explicit finite volume method. Based on observed data during the flood periods in 1996 and 1998, the model was calibrated and validated, and the results show that the model is effective and has high accuracy. In addition, the one-dimensional mathematical model for the river network and the horizontal two-dimensional (2-D) mathematical model for the Jingjiang flood diversion area were coupled to simulate the flood process in the Jingjiang River, Dongting Lake, and the Jingjiang flood diversion area. The calculated results of the coupled model are consistent with the practical processes. Meanwhile, the results show that the flood diversion has significant effects on the decrease of the peak water level at the Shashi and Chenjiawan hydrological stations near the flood diversion gates, and the effect is more obvious in the downstream than in the upstream.

Modelling the Hydraulic Behaviour of Growing Media with the Explicit Finite Volume Solution

The increasing imperviousness of urban areas reduces the infiltration and evapotranspiration capacity of urban catchments and results in increased runoff. In the last few decades, several solutions and techniques have been proposed to prevent such impacts by restoring the hydrological cycle. A limiting factor in spreading the use of such systems is the lack of proper modelling tools for design, especially for the infiltration processes in a growing medium. In this research, a physically-based model, employing the explicit Finite Volume Method (FVM), is proposed for modelling infiltration into growing media. The model solves a modified version of the Richards equation using a formulation which takes into account the main characteristics of green infrastructure substrates. The proposed model was verified against the HYDRUS-1D software and the comparison of results confirmed the suitability of the proposed model for correctly describing the hydraulic behaviour of soil substrates.

Flow separation control over airfoils using DBD plasma body force

The body force effects of plasma origin on the flow over a NACA 0015 airfoil are investigated by numerical simulation. The plasma actuator effect is estimated based on a phenomenological DBD plasma model coupled with 2-dimentional compressible Navier–Stokes equations. The equations are solved using an explicit finite volume method on unstructured grids. The responses of a separated flow field to the effects of a plasma actuator body force in various magnitudes and locations are presented. Also the effects of plasma region dimensions on the flow separation control are studied. It is found that the dimensions of plasma region, the magnitude of the body force, and the location of the plasma actuator all have significant impacts on the separation control.

Reactive Transport in Fractured Permeable Porous Media

AbstractThe transport of reactive solutes can be influenced by transport-related and sorption-related nonequilibrium processes. The reactive contaminant transport model for fracture and the multiprocess nonequilibrium (MPNE) model for porous formation is considered. Two coupled transport equations, one for the porous formation and the other for the fracture, were solved numerically using a hybrid finite-volume method. The numerical model employs a globally second-order accurate explicit finite-volume method for the advective transport and a finite-difference method for the dispersive transport and coupled reaction terms. An attempt is made to investigate the effects of various MPNE model parameters on the concentration profile in the fracture. It was found that the higher values of mass transfer coefficient, sorption coefficient, matrix diffusion coefficient, fracture retardation coefficient, and matrix porosity in the advective and nonadvective regions of the porous matrix leads to a decrease in the solu...

Analysis of non-Fourier conduction and radiation in a differentially heated 2-D square cavity

Combined mode conduction and radiation heat transfer in a 2-D square enclosure is analyzed. Time lag between the imposition of a discrete thermal disturbance on the north boundary, and manifestation of its effect is accounted by considering finite propagation speed of the conduction wave front. Optically absorbing, emitting and scattering nature of the medium necessitates consideration of the volumetric radiative term in the governing hyperbolic energy equation. With the volumetric radiative source term needed in the energy equation computed using the modified discrete ordinate method, effectiveness of the solvers like the alternative direction implicit scheme and the explicit finite volume method with minmod, MUSCL and superbee flux limiters in solving the hyperbolic energy equation is discussed. Without inducing excessive dissipation, the finite volume method with superbee flux limiter has been found to be the most effective in eliminating the spurious oscillations near the thermal shock front. Effects of optical thickness, scattering albedo and non-Fourier radiation to conduction parameter on thermal field are analyzed.

Integrating 1D and 2D hydrodynamic, sediment transport model for dam-break flow using finite volume method

The purpose of this study is to set up a dynamically linked 1D and 2D hydrodynamic and sediment transport models for dam break flow. The 1D-2D coupling model solves the generalized shallow water equations, the non-equilibrium sediment transport and bed change equations in a coupled fashion using an explicit finite volume method. It considers interactions among transient flow, strong sediment transport and rapid bed change by including bed change and variable flow density in the flow continuity and momentum equations. An unstructured Quadtree rectangular grid with local refinement is used in the 2D model. The intercell flux is computed by the HLL approximate Riemann solver with shock captured capability for computing the dry-to-wet interface for all models. The effects of pressure and gravity are included in source term in this coupling model which can simplify the computation and eliminate numerical imbalance between source and flux terms. The developed model has been tested against experimental and real-life case of dam-break flow over fix bed and movable bed. The results are compared with analytical solution and measured data with good agreement. The simulation results demonstrate that the coupling model is capable of calculating the flow, erosion and deposition for dam break flows in complicated natural domains.

Numerical modelling of non-cohesive embankment breach with the dual-mesh approach

The numerical model BASEMENT, based on the two-dimensional shallow-water equations, is applied to breaching processes of non-cohesive earth embankments due to overtopping. The governing equations are solved using an explicit finite-volume method combined with a Godunov-type approach. For spatial discretization, a mass-conserving dual-mesh approach with separate, unstructured meshes for hydrodynamic and sediment computations is developed allowing for accurate terrain representation. The surface erosion is modelled with the Exner and sorting equations for multiple grain classes in combination with empirical bed-load transport formulas and advection–diffusion equations for suspended-load transport. Additionally, the lateral breach widening caused by gravitationally-induced slope failures is considered using a novel algorithm adapted for unstructured grids. The model is successfully applied to two recent laboratory experiments including plane and spatial dike breaches, and a field-scale embankment breach. Detailed comparisons between measured and simulated laboratory spatial breach formations confirm the basic model assumptions.

A depth-averaged 2D shallow water model for breaking and non-breaking long waves affected by rigid vegetation

This paper presents a depth-averaged two-dimensional shallow water model for simulating long waves in vegetated water bodies under breaking and non-breaking conditions. The effects of rigid vegetation are modelled in the form of drag and inertia forces as sink terms in the momentum equations. The drag coefficient is treated as a calibrated bulk constant and also determined using two empirical formulas as functions of stem Reynolds number, Froude number, and vegetation volume fraction. The governing equations are solved using an explicit finite-volume method based on rectangular mesh with the Harten, Lax, and van Leer approximate Riemann solver with second-order piecewise linear reconstruction for the streamwise convection fluxes, a second-order upwind scheme for the lateral convection fluxes, and a stable centred difference scheme for the water surface gradient terms. The model was tested using five laboratory experiments, including steady flow in a flume with alternate vegetation zones, solitary wave in a vegetated flatbed flume, long-wave runup on a partially-vegetated sloping beach, the dam-break wave overtopping an obstacle, and breaking the solitary wave on a sloping beach. The computed water levels, flow velocities, wave heights, and runups are in generally good agreement with experimental observations. The model was then applied to assess the hydrodynamic effectiveness and limitations of vegetation in coastal and river protection. It is shown that vegetation along the coastal shoreline has a positive benefit in reducing wave runup on sloping beaches, whereas vegetation in open channels causes conflicting impacts: reducing inundation in the downstream areas, but increasing flood risk in a certain distance upstream.

Preprocess static subdomain decomposition in practical cases of 2D unsteady hydraulic simulation

Explicit finite volume methods are frequently used and widely accepted in hydraulic models based on the shallow water approximation. The main drawback of the approach is the time step size limit imposed by the Courant–Friedrichs–Lewy numerical stability constraint. This leads to excessively long computational times in large scale cases of practical interest. At the same time, the accuracy of the numerical results is associated to the use of fine computational meshes able to achieve enough spatial resolution. Taking into account that hydraulic modelers do not have access, in general, to large computational facilities, suitable and useful parallelization techniques are required. Furthermore, if high performance computing facilities are used, it is usually necessary to provide an estimation of the requirements of computational load to cover the length of the simulation. In this work the suitability of a preprocess static subdomain decomposition is explored and presented as a promising strategy to improve the efficiency of 2D unsteady shallow water computational models over dry bed in medium scale computational facilities and, at the same time, is useful to provide a preprocess computational time estimation if large scale computational facilities are going to be used.

Numerical simulation and parametric study of a supersonic intake

A computational fluid dynamics code was developed to compute the flow inside and around a supersonic external compression axisymmetric intake. The code solves the Reynolds-averaged Navier–Stokes equations using an explicit finite volume method in a structured grid and uses the Baldwin–Lomax algebraic model to compute the turbulent viscosity coefficient. Experiments were performed to validate the predicted results and good agreements are achieved. In the next part of the research, a parametric study was undertaken using the designed base case at a constant Mach number of 2 and at 0° angle of attack. The effects of various important parameters such as free stream Mach number, spike deflection angle, and back pressure ratio on the total pressure recovery, mass flow ratio, flow distortion, and drag coefficient of the intake were then numerically investigated. The results showed that when the spike deflection angle of the intake was changed from 28° (designed base case) to 30°, the intake drag coefficient was reduced up to 9%. In addition, the intake performance degraded for very low values of the back pressure ratio.