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Volume Scheme (volume + scheme)
Kinds of Volume Scheme Selected AbstractsA numerical study of an unsteady laminar flow in a doubly constricted 3D vesselINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002B. V. Rathish Kumar Abstract Unsteady flow dynamics in doubly constricted 3D vessels have been investigated under pulsatile flow conditions for a full cycle of period T. The coupled non-linear partial differential equations governing the mass and momentum of a viscous incompressible fluid has been numerically analyzed by a time accurate Finite Volume Scheme in an implicit Euler time marching setting. Roe's flux difference splitting of non-linear terms and the pseudo-compressibility technique employed in the current numerical scheme makes it robust both in space and time. Computational experiments are carried out to assess the influence of Reynolds' number and the spacing between two mild constrictions on the pressure drop across the constrictions. The study reveals that the pressure drop across a series of mild constrictions can get physiologically critical and is also found to be sensitive both to the spacing between the constrictions and the oscillatory nature of the inflow profile. The flow separation zone on the downstream constriction is seen to detach from the diverging wall of the constriction leading to vortex shedding with 3D features earlier than that on the wall in the spacing between the two constrictions. Copyright © 2002 John Wiley & Sons, Ltd. [source] Study of non-Fickian diffusion problems with the potential field in the cylindrical co-ordinate systemINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003Han-Taw Chen Abstract The present study applies a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the effect of a potential field on the one-dimensional non-Fickian diffusion problems in the cylindrical co-ordinate system. The Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the resulting equations are discretized by the control volume scheme. The primary difficulty in dealing with the present problem is the suppression of numerical oscillations in the vicinity of sharp discontinuities. Results show that the present numerical results do not exhibit numerical oscillations and the potential field plays an important role in the present problem. The strength of the jump discontinuity can be reduced by increasing the value of the potential gradient. The propagation speed of mass wave is independent of the potential gradient and the boundary condition. Copyright © 2003 John Wiley & Sons, Ltd. [source] 1-D numerical modelling of shallow flows with variable horizontal densityINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 11 2010Feifei Zhang Leighton Abstract A1-D numerical model is presented for vertically homogeneous shallow flows with variable horizontal density. The governing equations represent depth-averaged mass and momentum conservation of a liquid,species mixture, and mass conservation of the species in the horizontal direction. Here, the term ,species' refers to material transported with the liquid flow. For example, when the species is taken to be suspended sediment, the model provides an idealized simulation of hyper-concentrated sediment-laden flows. The volumetric species concentration acts as an active scalar, allowing the species dynamics to modify the flow structure. A Godunov-type finite volume scheme is implemented to solve the conservation laws written in a deviatoric, hyperbolic form. The model is verified for variable-density flows, where analytical steady-state solutions are derived. The agreement between the numerical predictions and benchmark test solutions illustrates the ability of the model to capture rapidly varying flow features over uniform and non-uniform bed topography. A parameter study examines the effects of varying the initial density and depth in different regions. Copyright © 2009 John Wiley & Sons, Ltd. [source] Numerical simulation of a single bubble by compressible two-phase fluidsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2010Siegfried Müller Abstract The present work deals with the numerical investigation of a collapsing bubble in a liquid,gas fluid, which is modeled as a single compressible medium. The medium is characterized by the stiffened gas law using different material parameters for the two phases. For the discretization of the stiffened gas model, the approach of Saurel and Abgrall is employed where the flow equations, here the Euler equations, for the conserved quantities are approximated by a finite volume scheme, and an upwind discretization is used for the non-conservative transport equations of the pressure law coefficients. The original first-order discretization is extended to higher order applying second-order ENO reconstruction to the primitive variables. The derivation of the non-conservative upwind discretization for the phase indicator, here the gas fraction, is presented for arbitrary unstructured grids. The efficiency of the numerical scheme is significantly improved by employing local grid adaptation. For this purpose, multiscale-based grid adaptation is used in combination with a multilevel time stepping strategy to avoid small time steps for coarse cells. The resulting numerical scheme is then applied to the numerical investigation of the 2-D axisymmetric collapse of a gas bubble in a free flow field and near to a rigid wall. The numerical investigation predicts physical features such as bubble collapse, bubble splitting and the formation of a liquid jet that can be observed in experiments with laser-induced cavitation bubbles. Opposite to the experiments, the computations reveal insight to the state inside the bubble clearly indicating that these features are caused by the acceleration of the gas due to shock wave focusing and reflection as well as wave interaction processes. While incompressible models have been used to provide useful predictions on the change of the bubble shape of a collapsing bubble near a solid boundary, we wish to study the effects of shock wave emissions into the ambient liquid on the bubble collapse, a phenomenon that may not be captured using an incompressible fluid model. Copyright © 2009 John Wiley & Sons, Ltd. [source] Shallow flow simulation on dynamically adaptive cut cell quadtree gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2007Qiuhua Liang Abstract A computationally efficient, high-resolution numerical model of shallow flow hydrodynamics is described, based on dynamically adaptive quadtree grids. The numerical model solves the two-dimensional non-linear shallow water equations by means of an explicit second-order MUSCL-Hancock Godunov-type finite volume scheme. Interface fluxes are evaluated using an HLLC approximate Riemann solver. Cartesian cut cells are used to improve the fit to curved boundaries. A ghost-cell immersed boundary method is used to update flow information in the smallest cut cells and overcome the time step restriction that would otherwise apply. The numerical model is validated through simulations of reflection of a surge wave at a wall, a low Froude number potential flow past a circular cylinder, and the shock-like interaction between a bore and a circular cylinder. The computational efficiency is shown to be greatly improved compared with solutions on a uniform structured grid implemented with cut cells. Copyright © 2006 John Wiley & Sons, Ltd. [source] A combined vortex and panel method for numerical simulations of viscous flows: a comparative study of a vortex particle method and a finite volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Kwang-Soo Kim Abstract This paper describes and compares two vorticity-based integral approaches for the solution of the incompressible Navier,Stokes equations. Either a Lagrangian vortex particle method or an Eulerian finite volume scheme is implemented to solve the vorticity transport equation with a vorticity boundary condition. The Biot,Savart integral is used to compute the velocity field from a vorticity distribution over a fluid domain. The vorticity boundary condition is improved by the use of an iteration scheme connected with the well-established panel method. In the early stages of development of flows around an impulsively started circular cylinder, and past an impulsively started foil with varying angles of attack, the computational results obtained by the Lagrangian vortex method are compared with those obtained by the Eulerian finite volume method. The comparison is performed separately for the pressure fields as well. The results obtained by the two methods are in good agreement, and give a better understanding of the vorticity-based methods. Copyright © 2005 John Wiley & Sons, Ltd. [source] Finite volume solution of the Navier,Stokes equations in velocity,vorticity formulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2005Baoshan Zhu Abstract For the incompressible Navier,Stokes equations, vorticity-based formulations have many attractive features over primitive-variable velocity,pressure formulations. However, some features interfere with the use of the numerical methods based on the vorticity formulations, one of them being the lack of a boundary conditions on vorticity. In this paper, a novel approach is presented to solve the velocity,vorticity integro-differential formulations. The general numerical method is based on standard finite volume scheme. The velocities needed at the vertexes of each control volume are calculated by a so-called generalized Biot,Savart formula combined with a fast summation algorithm, which makes the velocity boundary conditions implicitly satisfied by maintaining the kinematic compatibility of the velocity and vorticity fields. The well-known fractional step approaches are used to solve the vorticity transport equation. The paper describes in detail how we accurately impose no normal-flow and no tangential-flow boundary conditions. We impose a no-flux boundary condition on solid objects by the introduction of a proper amount of vorticity at wall. The diffusion term in the transport equation is treated implicitly using a conservative finite update. The diffusive fluxes of vorticity into flow domain from solid boundaries are determined by an iterative process in order to satisfy the no tangential-flow boundary condition. As application examples, the impulsively started flows through a flat plate and a circular cylinder are computed using the method. The present results are compared with the analytical solution and other numerical results and show good agreement. Copyright © 2005 John Wiley & Sons, Ltd. [source] Solution of the hyperbolic mild-slope equation using the finite volume methodINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003J. Bokaris Abstract A finite volume solver for the 2D depth-integrated harmonic hyperbolic formulation of the mild-slope equation for wave propagation is presented and discussed. The solver is implemented on unstructured triangular meshes and the solution methodology is based upon a Godunov-type second-order finite volume scheme, whereby the numerical fluxes are computed using Roe's flux function. The eigensystem of the mild-slope equations is derived and used for the construction of Roe's matrix. A formulation that updates the unknown variables in time implicitly is presented, which produces a more accurate and reliable scheme than hitherto available. Boundary conditions for different types of boundaries are also derived. The agreement of the computed results with analytical results for a range of wave propagation/transformation problems is very good, and the model is found to be virtually paraxiality-free. Copyright © 2003 John Wiley & Sons, Ltd. [source] A finite volume solver for 1D shallow-water equations applied to an actual riverINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2002N. Gouta Abstract This paper describes the numerical solution of the 1D shallow-water equations by a finite volume scheme based on the Roe solver. In the first part, the 1D shallow-water equations are presented. These equations model the free-surface flows in a river. This set of equations is widely used for applications: dam-break waves, reservoir emptying, flooding, etc. The main feature of these equations is the presence of a non-conservative term in the momentum equation in the case of an actual river. In order to apply schemes well adapted to conservative equations, this term is split in two terms: a conservative one which is kept on the left-hand side of the equation of momentum and the non-conservative part is introduced as a source term on the right-hand side. In the second section, we describe the scheme based on a Roe Solver for the homogeneous problem. Next, the numerical treatment of the source term which is the essential point of the numerical modelisation is described. The source term is split in two components: one is upwinded and the other is treated according to a centred discretization. By using this method for the discretization of the source term, one gets the right behaviour for steady flow. Finally, in the last part, the problem of validation is tackled. Most of the numerical tests have been defined for a working group about dam-break wave simulation. A real dam-break wave simulation will be shown. Copyright © 2002 John Wiley & Sons, Ltd. [source] An upwind finite volume scheme and its maximum-principle-preserving ADI splitting for unsteady-state advection-diffusion equationsNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 2 2003Hong Wang Abstract We develop an upwind finite volume (UFV) scheme for unsteady-state advection-diffusion partial differential equations (PDEs) in multiple space dimensions. We apply an alternating direction implicit (ADI) splitting technique to accelerate the solution process of the numerical scheme. We investigate and analyze the reason why the conventional ADI splitting does not satisfy maximum principle in the context of advection-diffusion PDEs. Based on the analysis, we propose a new ADI splitting of the upwind finite volume scheme, the alternating-direction implicit, upwind finite volume (ADFV) scheme. We prove that both UFV and ADFV schemes satisfy maximum principle and are unconditionally stable. We also derive their error estimates. Numerical results are presented to observe the performance of these schemes. © 2003 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 19: 211,226, 2003 [source] Hybrid finite element/volume method for shallow water equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2010Shahrouz Aliabadi Abstract A hybrid numerical scheme based on finite element and finite volume methods is developed to solve shallow water equations. In the recent past, we introduced a series of hybrid methods to solve incompressible low and high Reynolds number flows for single and two-fluid flow problems. The present work extends the application of hybrid method to shallow water equations. In our hybrid shallow water flow solver, we write the governing equations in non-conservation form and solve the non-linear wave equation using finite element method with linear interpolation functions in space. On the other hand, the momentum equation is solved with highly accurate cell-center finite volume method. Our hybrid numerical scheme is truly a segregated method with primitive variables stored and solved at both node and element centers. To enhance the stability of the hybrid method around discontinuities, we introduce a new shock capturing which will act only around sharp interfaces without sacrificing the accuracy elsewhere. Matrix-free GMRES iterative solvers are used to solve both the wave and momentum equations in finite element and finite volume schemes. Several test problems are presented to demonstrate the robustness and applicability of the numerical method. Copyright © 2010 John Wiley & Sons, Ltd. [source] Discrete duality finite volume schemes for two-dimensional drift-diffusion and energy-transport modelsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2009C. Chainais-Hillairet Abstract The drift-diffusion and the energy-transport models appear in the modelling of semiconductor devices. The main difficulty arising in the approximation of the energy transport model by finite volume schemes is the discretization of the Joule heating term in the equation on the density of energy. Following some recent ideas by Domelevo and Omnès for the discretization of the Laplace equation on almost general meshes, we construct a finite volume approximation of the 2-D drift-diffusion and energy transport models. These schemes still hold on almost general meshes. Finally, we present numerical simulations of semiconductor devices. Copyright © 2006 John Wiley & Sons, Ltd. [source] Fourier analysis of a class of upwind schemes in shallow water systems for gravity and Rossby wavesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008A. M. Mohammadian Abstract A Fourier analysis has been performed for a class of upwind finite volume schemes, including the study of phase speed, group velocity, damping and dispersion. In the first part, pure gravity waves are investigated. As expected, most upwind schemes lead to a significant damping, but they exhibit a better phase behavior than most centered schemes. In the second part, the Coriolis parameter is considered and the Rossby modes are studied. In this case, all selected upwind schemes lead to a severe damping. The numerical results are also compared with those obtained by using a slope limiter approach. It is concluded that most upwind schemes with or without slope limiters present poor results for an accurate calculation of the Rossby modes. Copyright © 2008 John Wiley & Sons, Ltd. [source] Some recent finite volume schemes to compute Euler equations using real gas EOSINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2002T. Gallouët Abstract This paper deals with the resolution by finite volume methods of Euler equations in one space dimension, with real gas state laws (namely, perfect gas EOS, Tammann EOS and Van Der Waals EOS). All tests are of unsteady shock tube type, in order to examine a wide class of solutions, involving Sod shock tube, stationary shock wave, simple contact discontinuity, occurrence of vacuum by double rarefaction wave, propagation of a one-rarefaction wave over ,vacuum', , Most of the methods computed herein are approximate Godunov solvers: VFRoe, VFFC, VFRoe ncv (,, u, p) and PVRS. The energy relaxation method with VFRoe ncv (,, u, p) and Rusanov scheme have been investigated too. Qualitative results are presented or commented for all test cases and numerical rates of convergence on some test cases have been measured for first- and second-order (Runge,Kutta 2 with MUSCL reconstruction) approximations. Note that rates are measured on solutions involving discontinuities, in order to estimate the loss of accuracy due to these discontinuities. Copyright © 2002 John Wiley & Sons, Ltd. [source] High-order filtering for control volume flow simulationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 7 2001G. De Stefano Abstract A general methodology is presented in order to obtain a hierarchy of high-order filter functions, starting from the standard top-hat filter, naturally linked to control volumes flow simulations. The goal is to have a new filtered variable better represented in its high resolved wavenumber components by using a suitable deconvolution. The proposed formulation is applied to the integral momentum equation, that is the evolution equation for the top-hat filtered variable, by performing a spatial reconstruction based on the approximate inversion of the averaging operator. A theoretical analysis for the Burgers' model equation is presented, demonstrating that the local de-averaging is an effective tool to obtain a higher-order accuracy. It is also shown that the subgrid-scale term, to be modeled in the deconvolved balance equation, has a smaller absolute importance in the resolved wavenumber range for increasing deconvolution order. A numerical analysis of the procedure is presented, based on high-order upwind and central fluxes reconstruction, leading to congruent control volume schemes. Finally, the features of the present high-order conservative formulation are tested in the numerical simulation of a sample turbulent flow: the flow behind a backward-facing step. Copyright © 2001 John Wiley & Sons, Ltd. [source] | ||||||||||