Hybrid Finite Volume Method Research Articles

A simple hybrid finite volume solver for compressible turbulence

SummaryA simple, explicit, hybrid finite volume method for simulating compressible turbulence is developed by combining a fourth‐order central scheme and a shock‐capturing simple low‐dissipation advection upstream splitting method. The total flux on each of the cell faces is computed as a weighted average of central/nondissipative and upwind/dissipative fluxes. The weights are determined using an unphysical oscillation sensor in addition to a more traditional discontinuity sensor used in earlier studies. Shocks are well captured, but overshoots in density are predicted around contact discontinuities that are normal to the flow. The use of the latter sensor effectively prevents these overshoots from generating spurious oscillations that travel away from the contact lines. The efficacy of the proposed method for direct or large‐eddy simulations of supersonic turbulence is established using several canonical test problems. Copyright © 2015 John Wiley & Sons, Ltd.

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...

Effects of geomechanical changes on the validity of a discrete fracture network representation of a realistic two-dimensional fractured rock

This paper aims to examine the validity of the discrete fracture network (DFN) method in representing a realistic two-dimensional fractured rock in terms of their geomechanical response to in-situ stresses and hydraulic behaviour in a steady state fluid field. First, a real fracture network is extracted from the geological map of an actual rock outcrop, which is termed the analogue fracture network (AFN). Multiple DFN realisations are created using the statistics of the analogue pattern. A conductivity parameter that was found to have a linear relationship with the conductivity of 2D fracture networks is included to further enhance network similarity. A series of numerical experiments are designed with far-field stresses applied at a range of angles to the rock domains and their geomechanical response is modelled using the combined finite-discrete element method (FEMDEM). A geomechanical comparison between the AFN and its DFN equivalents is made based on phenomena such as heterogeneity of fracture-dependent stress contours, sliding between pre-existing fracture walls, coalescence of propagating fractures and variability of aperture distribution. Furthermore, an indirect hydro-mechanical (HM) coupling is applied and the hydraulic behaviour of the porous rock models is investigated using the hybrid finite element-finite volume method (FEFVM). A further comparison is conducted focusing on the hydraulic behaviour of the AFN and DFNs under the effects of geomechanical changes. The results show that although DFNs may represent an AFN quite well for fixed mechanical conditions, such a representation may not be dependable if mechanical changes occur.

Finite volume model for reactive transport in fractured porous media with distance- and time-dependent dispersion

There are very few studies of fractured porous media that use distance- and time-dependent dispersion models, and, to the best of our knowledge, none which compare these with constant dispersion models. Therefore, in this study, the behaviour of temporal and spatial concentration profiles with distance- and time-dependent dispersion models is investigated. A hybrid finite volume method is used to solve the governing equations for these dispersion models. The developed numerical model is used to study the effects of matrix diffusion coefficient, groundwater velocity and matrix and fracture retardation factor on concentration profiles in the application of constant, distance-dependent and time-dependent dispersion models. In addition, an attempt is made to evaluate the applicability of these dispersion models by using the models to simulate experimental data. It was found that a better fit to the observed data is obtained in the case of distance- and time-dependent dispersion models as compared to the constant dispersion model. Thus, these numerical experiments indicate that distance- and time-dependent dispersion models have better simulation potential than the constant dispersion model.

An Arbitrary-Order and Compact-Stencil Discretization of Diffusion on General Meshes Based on Local Reconstruction Operators

Abstract We develop an arbitrary-order primal method for diffusion problems on general polyhedral meshes. The degrees of freedom are scalar-valued polynomials of the same order at mesh elements and faces. The cornerstone of the method is a local (elementwise) discrete gradient reconstruction operator. The design of the method additionally hinges on a least-squares penalty term on faces weakly enforcing the matching between local element- and face-based degrees of freedom. The scheme is proved to optimally converge in the energy norm and in the L2 -norm of the potential for smooth solutions. In the lowest-order case, equivalence with the Hybrid Finite Volume method is shown. The theoretical results are confirmed by numerical experiments up to order 4 on several polygonal meshes.

A $$P_N P_M{-} CPR $$ P N P M - C P R Framework for Hyperbolic Conservation Laws

The correction procedure via reconstruction (CPR) method is a discontinuous nodal formulation unifying several well-known methods in a simple finite difference like manner. The $$P_NP_M{-} CPR $$ P N P M - C P R formulation is an extension of $$P_NP_M$$ P N P M or the reconstructed discontinuous Galerkin (RDG) method to the CPR framework. It is a hybrid finite volume and discontinuous Galerkin (DG) method, in which neighboring cells are used to build a higher order polynomial than the solution representation in the cell under consideration. In this paper, we present several $$P_NP_M$$ P N P M schemes under the CPR framework. Many interesting schemes with various orders of accuracy and efficiency are developed. The dispersion and dissipation properties of those methods are investigated through a Fourier analysis, which shows that the $$P_NP_M{-} CPR $$ P N P M - C P R method is dependent on the position of the solution points. Optimal solution points for 1D $$P_NP_M{-} CPR $$ P N P M - C P R schemes which can produce expected order of accuracy are identified. In addition, the $$P_NP_M{-} CPR $$ P N P M - C P R method is extended to solve 2D inviscid flow governed by the Euler equations and several numerical tests are performed to assess its performance.

Hybrid Lattice Boltzmann and Finite Volume Method for Natural Convection

A hybrid lattice Boltzmann and finite volume method is proposed for fluid flow and heat transfer simulation. The lattice Boltzmann method was applied to obtain the velocity field, whereas the finite volume method was used to obtain the temperature field. The two-dimensional nine discrete velocities (D2Q9) model and nonequilibrium extrapolation scheme boundary condition were used in the lattice Boltzmann method, and the SIMPLE algorithm with the QUICK scheme was employed in the finite volume method. Natural convection with different Rayleigh numbers was solved by the hybrid method, and the results agreed very well with those obtained from a pure finite volume method and pure thermal lattice Boltzmann method. This is the first time that the hybrid lattice Boltzmann with the finite volume method has been applied to solve natural convection problem.

Numerical Simulation of Natural Flow of Air Through a Room

A computational model for the analysis of natural flow of air through a ventilation system has been presented. The model has been validated and applied for the analysis of solar heat driven flow of air through a typical ventilated room space. Computations have been performed for Rayleigh number (dimensionless number characterizing this flow) ranging from . The details of the flow and temperature distributions in the room have been extracted corresponding to air as the working medium. This paper presents the details of the computational model and results corresponding to different conditions. The numerical method used is a hybrid finite element-finite volume method.

Numerical study of natural convection from a heat generating element using a locally divergence free FEM and comparison with experiment

A locally divergence free numerical scheme based on a hybrid finite element-finite volume method together with a restricted domain approach is used for the numerical solution of laminar conjugate natural convection in a vertical channel containing a short planar heat generating element. Numerical simulations have been carried out for modified Rayleigh numbers in the range 1×105–8.1×107. The numerically evaluated temperature rise above the ambient of the heat generating element is found to agree well with experimental data. A correlation for dimensionless temperature rise as a function of dimensionless volumetric heat generation is presented. Natural convection, Hybrid FEM-FVM method, Restricted domain approach, Volumetric heat generation.

The Analysis of Flow Characteristics for the High-Speed Train with Strong Crosswind Using CFD

High-speed trains are easily got overturned in strong crosswind. This paper aims to analyze the fluid field of high-speed train under different distortion angles by using computational fluid dynamics (CFD), hybrid grid method and finite volume method. The results shows that the vortexes roll by the separated airflow are alternating occur and develop along the body from the top and bottom. It causes a strong affect to the lateral stability of the train.

Efficient Field-Scale Simulation of Black Oil in a Naturally Fractured Reservoir Through Discrete Fracture Networks and Homogenized Media

SummaryThis paper describes a hybrid finite volume method, designed to simulate multiphase flow in a field-scale naturally fractured reservoir. Lee et al. (WRR 37:443-455, 2001) developed a hierarchical approach in which the permeability contribution from short fractures is derived in an analytical expression that from medium fractures is numerically solved using a boundary element method. The long fractures are modeled explicitly as major fluid conduits. Reservoirs with well-developed natural fractures include many complex fracture networks that cannot be easily modeled by simple long fracture formulation and/or homogenized single continuity model. We thus propose a numerically efficient hybrid method in which small and medium fractures are modeled by effective permeability, and large fractures are modeled by discrete fracture networks. A simple, systematic way is devised to calculate transport parameters between fracture networks and discretized, homogenized media. An efficient numerical algorithm is also devised to solve the dual system of fracture network and finite volume grid. Black oil formulation is implemented in the simulator to demonstrate practical applications of this hybrid finite volume method.

Hybrid Unsteady RANS and PDF Method for Turbulent Non-Reactive and Reactive Flows

A hybrid unsteady Reynolds-averaged numerical simulation (U-RANS) and probability density function (PDF) method is developed for turbulent non-reactive and reactive flows. The resulting modeled equations are solved by a consistent hybrid finite volume and Lagrangian Monte-Carlo particle method. Both turbulent non-reactive and reactive flows in a rectangular channel containing a triangular-shaped bluff-body are simulated. One-step and two-step mechanisms for propane/air combustion are used for the reactive case. The time-averaged results are compared with both experimental data and numerical results from the literature using large eddy simulation (LES) and steady RANS. The results of the present method are in good agreement with the experimental data, and they improve the numerical results available in the literature.

On the Computation of Compressible Turbulent Flows on Unstructured Grids

An accurate, fast, matrix-free implicit method has been developed to solve compressible turbulent How problems using the Spalart and Allmaras one equation turbulence model on unstructured meshes. The mean-flow and turbulence-model equations are decoupled in the time integration in order to facilitate the incorporation of different turbulence models and reduce memory requirements. Both mean flow and turbulent equations are integrated in time using a linearized implicit scheme. A recently developed, fast, matrix-free implicit method, GMRES+LU-SGS, is then applied to solve the resultant system of linear equations. The spatial discretization is carried out using a hybrid finite volume and finite element method, where the finite volume approximation based on a containment dual control volume rather than the more popular median-dual control volume is used to discretize the inviscid fluxes, and the finite element approximation is used to evaluate the viscous flux terms. The developed method is used to compute a variety of turbulent flow problems in both 2D and 3D. The results obtained are in good agreement with theoretical and experimental data and indicate that the present method provides an accurate, fast, and robust algorithm for computing compressible turbulent flows on unstructured meshes.