Narrow Results

In the present paper, a comparative study of numerical solutions for steady flows with heat transfer based on the finite volume method (FVM) and the relatively new lattice Boltzmann method (LBM) is presented. In the last years, the LB methods have challenged the classical FV methods to solve the Navier–Stokes equations and have proven to be superior in accuracy and efficiency for certain applications. Most of these studies were related to the transport of mass and momentum. In the meantime, significant effort has been invested in the application of the LBM to simulate flows including heat transfer. The studies in the present paper are the analysis of performance and accuracy aspects of LBM applied to the prediction of these flows. For a fully developed laminar flow between parallel plates, analytical solutions for the heat transfer in fully developed thermal boundary layers are available and may be compared with the respective numerical results. Finally, a hybrid approach is proposed to circumvent numerical problems of the thermal LB methods.

A lattice Boltzmann model using upstream finite volume scheme has been employed in the investigation of bifurcation and transition of flow through suddenly-expanded channels. To enhance the stability and accuracy of simulation, a fifth-order Runge–Kutta method is used for the time-marching and upwind biasing factors based on pressure are used as flux correctors in the lattice Boltzmann equation. In the range of Reynolds numbers investigated, the laminar flow through the expansion underwent a symmetry-breaking bifurcation. The critical Reynolds number evaluated from the experiments and the simulations were compared to other values reported in the literature. Comparisons are found to be quantitatively accurate. Furthermore, the results show that the critical Reynolds number decreases with increasing channel expansion ratio. At a fixed supercritical Reynolds number, the location at which the jet first impinges on the channel wall grows with the expansion ratio.

The thermal performance of two-dimensional (2D) field-effect transistors (FET) is investigated frequently by solving the Fourier heat diffusion law and the Boltzmann transport equation (BTE). With the introduction of the new generation of 3D FETs in which their thickness is less than the phonon mean-free-path it is necessary to carefully simulate the thermal performance of such devices. This paper numerically integrates the BTE in common 2D transistors including planar single layer and Silicon-On-Insulator (SOI) transistor, and the new generation of 3D transistors including FinFET and Tri-Gate devices. In order to decrease the directional dependency of results in 3D simulations; the Legendre equal-weight (P_N-EW) quadrature set has been employed. It is found that if similar switching time is assumed for 3D and 2D FETs while the new generation of 3D FETs has less net energy consumption, they have higher hot-spot temperature. The results show continuous heat flux distribution normal to the silicon/oxide interface while the temperature jump is seen at the interface in double layer transistors.

This paper uses the finite volume lattice Boltzmann method (FVLBM) to simulate the transient heat conduction from macro- to nano-scales corresponding to Kn = 0.01–10. This model is used for two dimensional (2D) transient hotspot modeling. The results of the diffusive regime are compared with those of the Fourier law as a model of continuum mechanics and an excellent agreement is found in this regime. After the validation of model for the case of Kn = 0.01, it has been used for high-Knudsen number simulations and a test case with Kn = 10 is studied. By increasing the Knudsen number from 0.01 up to 10, the transition from totally diffusive to totally ballistic behavior has been discussed and the wave-feature of heat transport through the solid material has been investigated.

We study here a model of conservative nonlinear conservation law with a flux function with discontinuous coefficients, namely the equation u_t + (k(x)u(1 - u))_x = 0. It is a particular entropy condition on the line of discontinuity of the coefficient k which ensures the uniqueness of the entropy solution. This condition is discussed and justified. On the other hand, we perform a numerical analysis of the problem. Two finite volume schemes, the Godunov scheme and the VFRoe-ncv scheme, are proposed to simulate the conservation law. They are compared with two finite volume methods classically used in an industrial context. Several tests confirm the good behavior of both new schemes, especially through the discontinuity of permeability k (whereas a loss of accuracy may be detected when industrial methods are performed). Moreover, a modified MUSCL method which accounts for stationary states is introduced.

The present paper is devoted to the computation of two-phase flows using the two-fluid approach. The overall model is hyperbolic and has no conservative form. No instantaneous local equilibrium between phases is assumed, which results in a two-velocity two-pressure model. Original closure laws for interfacial velocity and interfacial pressure are proposed. These closures allow to deal with discontinuous solutions such as shock waves and contact discontinuities without ambiguity with the definition of Rankine–Hugoniot jump relations. Each field of the convective system is investigated, providing maximum principle for the volume fraction and the positivity of densities and internal energies are ensured when focusing on the Riemann problem. Two-finite volume methods are presented, based on the Rusanov scheme and on an approximate Godunov scheme. Relaxation terms are taken into account using a fractional step method. Eventually, numerical tests illustrate the ability of both methods to compute two-phase flows.

In this work we present some moment preserving finite volume schemes (FVS) for solving population balance equations. We are considering unified numerical methods to simultaneous aggregation, breakage, growth and source terms, e.g. for nucleation. The criteria for the preservation of different moments are given. The property of conservation is a special case of preservation. First we present a FVS which shows the preservation with respect to one-moment depending upon the processes under consideration. In case of the aggregation and breakage it satisfies first-moment preservation whereas for the growth and nucleation we observe zeroth-moment preservation. This is due to the well-known property of conservativity of FVS. However, coupling of all the processes shows no preservation for any moments. To overcome this issue, we reformulate the cell average technique into a conservative formulation which is coupled together with a modified upwind scheme to give moment preservation with respect to the first two-moments for all four processes under consideration. This allows for easy coupling of these processes. The preservation is proven mathematically and verified numerically. The numerical results for the first two-moments are verified for various coupled processes where analytical solutions are available.

This paper deals with construction and convergence analysis of a finite volume scheme for compressible/incompressible (gas–water) flows in porous media. The convergence properties of finite volume schemes or finite element scheme are only known for incompressible fluids. We present a new result of convergence in a two or three dimensional porous medium and under the only consideration that the density of gas depends on global pressure. In comparison with incompressible fluid, compressible fluids requires more powerful techniques; especially the discrete energy estimates are not standard.

We study the qualitative convergence behavior of a novel FV-discretization scheme of the Fokker–Planck equation, the squareroot approximation scheme (SQRA), that recently was proposed by Lie, Fackeldey and Weber [A square root approximation of transition rates for a markov state model, SIAM J. Matrix Anal. Appl.34 (2013) 738–756] in the context of conformation dynamics. We show that SQRA has a natural gradient structure and that solutions to the SQRA equation converge to solutions of the Fokker–Planck equation using a discrete notion of G-convergence for the underlying discrete elliptic operator. The SQRA does not need to account for the volumes of cells and interfaces and is tailored for high-dimensional spaces. However, based on FV-discretizations of the Laplacian it can also be used in lower dimensions taking into account the volumes of the cells. As an example, in the special case of stationary Voronoi tessellations, we use stochastic two-scale convergence to prove that this setting satisfies the G-convergence property.

This paper presents details of finite volume and finite element numerical models based on unstructured triangular meshes that are used to solve the two-dimensional nonlinear shallow water equations (SWEs). The finite volume scheme uses Roe's approximate Riemann solver to evaluate the convection terms. Second order accuracy is achieved by means of the MUSCL approach with MinMod and VanAlbada limiters. The finite element model utilizes the Lax–Wendroff two-step scheme, which is second-order in space and time. The models are validated and their relative performance compared for several benchmark problems, including a hydraulic jump, and flows in converging and converging–diverging channels.

This article presents the application of a RANS algorithm based on a pressure correction method for incompressible flow simulations of low-speed rotating machines. A numerical scheme is developed by extending a flow analysis in a stationary frame to a rotating frame for turbomachinery applications. The numerical scheme is explained with emphasis on the effect of rotation on the flow fields and turbulence modeling. The results of the numerical calculations for flow through an enclosed turbomachine and an extended turbomachine are compared with the experimental data to judge them on realistic flow patterns. The numerical solutions have shown reasonable agreement with the experimental data which demonstrates the merits and robustness of this numerical scheme.

In this paper, two dimensional unsteady flow and energy equations are employed for simulating the fluid flow, heat transfer and solidification during direct chill continuous casting of Al-Mg alloy billet. In these processes, the formation of some macro defects such as thermal cracking, hot tearing, surface cracking, etc, has been found to initiate during the starting phase of the operation. In this paper, a numerical study of these developing fluid flow and thermal phenomena from the beginning of casting operation to a steady-state is presented. The computations are based on an iterative deforming finite volume method and a single-domain enthalpy formulation to solve the growth of metal being solidified and the accompanying dynamic fluid flow and thermal behavior. The effect of phase change on convection is accounted for using a Darcy's law-type porous media treatment. The results indicate that the fluid flow and temperature fields change drastically at the initial stage but evolve slowly afterwards.

Line-by-line (LBL) solution method is a numerical and semidirect method, which can be applied for solving algebraic equation set resulted from discretization. In this article, the effect of solution arrangement of the grids (SAG) on accuracy of diffusion equation's solution has been investigated. First of all, diffusion equation had been discrete by finite volume method; in the second place, MATLAB software has been exploited for writing a code for solving algebraic equation set by using LBL solution method with alternative SAG. In the third place, for examining the effect of SAG, water seepage through foundations of several concrete dams was modeled with this code. In addition, these dams were modeled in SEEP/W 2004 and PHASE2 6.0 software, as support. Finally, we drew an analogy between the results by Mann–Whitney U statistical test with SPSS 14 software. Comparison of the results revealed that SAGs have affected P-value up to 39%. As a result, the most accurate SAGs had been decided by the problem geometry. Furthermore, the result of the finite volume and finite element methods had no statistical by significant difference. Moreover, convergence and convergence path had been dictated by problem geometry and SAGs.

This work presents computational simulations and analytical techniques for solving the drift-flux two-phase flow model. The model equations are formulated to describe the exact solution of the Riemann problem. The solution is constructed by solving the conservation of mass for each phase and the mixture conservation momentum equation of the two phases under isothermal conditions. Particular attention is given to address the expressions for jump relationships and the Riemann invariants. The performance of the developed Riemann solver is assessed with respect to different test cases selected from the literature. Comparisons with Godunov methods of centred-type are provided to demonstrate the use of the proposed exact and computational framework. Excellent agreement is observed between analytical results and numerical predictions.

In this study, the Lattice Boltzmann Method (LBM) is implemented through a finite-volume approach to perform 2D, incompressible, and time-accurate fluid flow analyses on structured grids. Compared to the standard LBM (the so-called stream and collide scheme), the finite-volume approach followed in this study necessitates more computational effort, but the major limitations of the former on grid uniformity and Courant–Friedrichs–Lewy (CFL) number that is to be one are removed. Even though these improvements pave the way for the possibility of solving more practical fluid flow problems with the LBM, time-accurate simulations are still restricted due to the stability criteria dictated by high-aspect ratio grid cells that are usually required for adequate resolution of boundary layers and the stiffness due to the nature of the equation that are being solved. To overcome this limitation, a Dual Time Stepping (DTS) scheme, which iterates the solution in pseudo time using an Implicit-Explicit (IMEX) Runge–Kutta method while advancing the solution in physical time with an explicit scheme (backward difference formula), is developed and implemented. The accuracy of the resulting flow solver is evaluated using benchmark flow problems and overall second-order accuracy is demonstrated.

A numerical model for the prediction of storm surges over complex landscapes is assembled using state-of-the-art techniques. The model is based on the full nonlinear depth-averaged long wave equations solved via an explicit finite volume scheme. The interfacial fluxes are computed from slope limited reconstructions of the state variables using Osher’s approximate Riemann solver. The geometric source terms are treated in a simple manner that is well balanced and consistent with the numerical flux. The numerical solution technique has been chosen to enable the accurate simulation of flows over complex topography. Importantly, the scheme conserves both mass and momentum even when the flow involves wetting–drying fronts. This approach makes the model extremely robust in cases that involve bathymetries which include large spatial gradients and even discontinuities. Another important feature of the model is the use of a simple underlying Cartesian mesh with quad-tree-based static and dynamic refinement. This permits the simulation of highly unsteady flows over complex landscapes (including localized features such as canals) by locally increasing (or relaxing) grid resolution in a dynamic fashion. If it is deemed desirable, the numerical and physical boundaries can be aligned. This alignment is achieved by a cut-cell-type approach in combination with quad-tree-based mesh refinement. In this paper, we describe the model and then present a number of tests that have been carefully chosen to verify various aspects of the solution algorithm.

Motivated by recent groundbreaking work of Ontaneda, we describe a sizable class of closed manifolds such that the product of each manifold in the class with ℝ admits a complete metric of bounded negative sectional curvature which is an exponentially warped near one end and has finite volume near the other end.

We investigate the and coupled channels system in a finite volume and study the properties of the Λ(1405) resonance. We calculate the energy levels in a finite volume and solve the inverse problem of determining the resonance position in the infinite volume. We devise the best strategy of analysis to obtain the two poles of the Λ(1405) in the infinite volume case, with sufficient precision to distinguish them.

We report on our study of low-lying resonances in ππ and Kπ scattering from lattice QCD. Based on ab-initio multi-hadron spectroscopy and the Lüscher finite-volume method, we have investigated the elastic scattering amplitudes for ππP-wave, KπS-wave and P-wave partial waves. A particular focus of the discussion will be the parametrizaton of the amplitudes with respect to the identification of resonance parameters. The shown results are obtained for two gauge field ensembles at pion masses 317 MeV and 178 MeV.

Lattice QCD simulation for hadron spectroscopy has reached three-body threshold. However, it is difficult to go further without an appropriate method to analyze the finite volume effect in three-body system. We derive the three-body quantization condition in a finite volume using an effective field theory in the particle-dimer picture. It is a powerful and transparent method to interpret three-body physical observables from lattice simulations. We review the whole method including formalism, quantization condition and the application for both 3-body bound states and scattering states.