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Numerical Scheme (numerical + scheme)
Selected AbstractsA conservative integral for bimaterial notches subjected to thermal stressesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2004Leslie Banks-Sills Abstract In this investigation, a conservative integral based on the Betti reciprocal principle is developed to obtain stress intensity factors for a bimaterial notch in which the body is subjected to a thermal load. The bonded materials are linear elastic, isotropic and homogeneous. According to the linear theory of elasticity, stresses in the neighbourhood of the notch tip are generally singular as a result of the mismatch of the elastic constants. Eigenvalues and eigenfunctions depend upon the mechanical properties and wedge angles. They may be real, complex or power-logarithmic. Real and complex eigenvalues are considered in this study. The stress intensity factor represents the amplitude of the stress singularity and depends upon material properties, geometry and load or temperature. Because of the highly singular behaviour of one of the integrals that is part of the conservative integral, the former is carried out by a hybrid analytical/numerical scheme. The finite element method is employed to obtain displacements caused by the temperature distribution in the body. The conservative integral is applied to several problems appearing in the literature. Both good agreement between those results and the ones obtained here, as well as path stability for all problems is attained. A wide range of material parameters is also studied. Copyright © 2004 John Wiley & Sons, Ltd. [source] Progressive collapse analysis through strength degradation and fracture in the Mixed Lagrangian FormulationEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 13 2009O. Lavan Abstract The dynamic analysis of progressive collapse faces a great number of obstacles that often lead to the collapse of the analysis prior to the actual analysis of collapse. Hence, the Mixed Lagrangian Formulation that has been shown to be very robust was adopted as a framework to accommodate such analysis. By modifying the loading function and the numerical scheme, the capabilities of this framework were extended to account for strength degradation and fracture, while some insight to its behavior is introduced as well. The examples presented show a very robust and stable behavior of the numerical scheme in terms of the time step size required, even in cases where a sudden fracture takes place. Copyright © 2009 John Wiley & Sons, Ltd. [source] Analysis and performance of a predictor-multicorrector Time Discontinuous Galerkin method in non-linear elastodynamicsEARTHQUAKE ENGINEERING AND STRUCTURAL DYNAMICS, Issue 10 2002Oreste S. Bursi Abstract A predictor-multicorrector implementation of a Time Discontinuous Galerkin method for non-linear dynamic analysis is described. This implementation is intended to limit the high computational expense typically required by implicit Time Discontinuous Galerkin methods, without degrading their accuracy and stability properties. The algorithm is analysed with reference to conservative Duffing oscillators for which closed-form solutions are available. Therefore, insight into the accuracy and stability properties of the predictor-multicorrector algorithm for different approximations of non-linear internal forces is gained, showing that the properties of the underlying scheme can be substantially retained. Finally, the results of representative numerical simulations relevant to Duffing oscillators and to a stiff spring pendulum discretized with finite elements illustrate the performance of the numerical scheme and confirm the analytical estimates. Copyright © 2002 John Wiley & Sons, Ltd. [source] Simulating the hydraulic characteristics of the lower Yellow River by the finite-volume techniqueHYDROLOGICAL PROCESSES, Issue 14 2002Qing Wan Abstract The finite-volume technique is used to solve the two-dimensional shallow-water equations on unstructured mesh consisting of quadrilateral elements. In this paper the algorithm of the finite-volume method is discussed in detail and particular attention is paid to accurately representing the complex irregular computational domain. The lower Yellow River reach from Huayuankou to Jiahetan is a typical meandering river. The generation of the computational mesh, which is used to simulate the flood, is affected by the distribution of water works in the river channel. The spatial information about the two Yellow River levee, the protecting dykes, and those roads that are obviously higher than the ground, need to be used to generate the computational mesh. As a result these dykes and roads locate the element interfaces of the computational mesh. In the model the finite-volume method is used to solve the shallow-wave equations, and the Osher scheme of the empirical function is used to calculate the flux through the interface between the neighbouring elements. The finite-volume method has the advantage of using computational domain with complex geometry, and the Osher scheme is a method based on characteristic theory and is a monotone upwind numerical scheme with high resolution. The flood event with peak discharge of 15 300 m3/s, occurring in the period from 30 July to 10 August 1982, is simulated. The estimated result indicates that the simulation method is good for routing the flood in a region with complex geometry. Copyright © 2002 John Wiley & Sons, Ltd. [source] Liquefaction and cyclic mobility model for saturated granular mediaINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 5 2006S. López-Querol Abstract A new constitutive law for the behaviour of undrained sand subjected to dynamic loading is presented. The proposed model works for small and large strain ranges and incorporates contractive and dilative properties of the sand into the unified numerical scheme. These features allow to correctly predict liquefaction and cyclic mobility phenomena for different initial relative densities of the soil. The model has been calibrated as an element test, by using cyclic simple shear data reported in the literature. For the contractive sand behaviour a well-known endochronic densification model has been used, whereas a plastic model with a new non-associative flow rule is applied when the sand tends to dilate. Both dilatancy and flow rule are based on a new state parameter, associated to the stiffness degradation of the material as the shaking goes on. Also, the function that represents the rearrangement memory of the soil takes a zero value when the material dilates, in order to easily model the change in the internal structure. Proceeding along this kind of approach, liquefaction and cyclic mobility are modelled with the same constitutive law, within the framework of a bi-dimensional FEM coupled algorithm developed in the paper. For calibration purposes, the behaviour of the soil in a cyclic simple shear test has been simulated, in order to estimate the influence of permeability, frequency of loading, and homogeneity of the shear stress field on the laboratory data. Copyright © 2006 John Wiley & Sons, Ltd. [source] Parameter sensitivity in finite element analysis with constitutive models of the rate typeINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 2 2006Wolfgang Fellin Abstract Non-linear soil,structure interactions are usually analysed using an incremental finite element approach. There a constitutive subroutine provides for each element the stress increment for a given strain increment. In geotechnical calculations, uncertainties in material parameters and initial conditions are abundant. Sensitivity analysis can be a first step to account for such uncertainties. Sensitivities of the system response with respect to material parameters and initial conditions can be calculated by differentiating the whole numerical scheme. It turns out that the essential information from the constitutive subroutine are the derivatives of the stress increment with respect to the strain increment, as well as the derivatives with respect to material parameters and all state variables involved in the problem. We propose a method to compute these quantities numerically for any constitutive model that can be written in rate form and for any suitable integrator of such a model. We further present a concise way to supply the output of the sensitivity analysis to the designing engineer. Our theoretical investigations are illustrated with element tests and with a typical geotechnical application. Copyright © 2005 John Wiley & Sons, Ltd. [source] Minimum principle and related numerical scheme for simulating initial flow and subsequent propagation of liquefied groundINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 11 2005Sami Montassar Abstract The problem of predicting the evolution of liquefied ground, modelled as a viscoplastic material, is addressed by combining a minimum principle for the velocity field, which characterizes such an evolution, and a time step integration procedure. Two different numerical schemes are then presented for the finite element implementation of this minimum principle, namely, the regularization technique and the decomposition-co-ordination method by augmented Lagrangian. The second method, which proves more accurate and efficient than the first, is finally applied to simulate the incipient flow failure and subsequent spreading of a liquefied soil embankment subject to gravity. The strong influence of liquefied soil residual shear strength on reducing the maximum amplitude of the ground displacement is particularly emphasized in such an analysis. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical modelling for earthquake engineering: the case of lightly RC structural wallsINTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS, Issue 7-8 2004J. Mazars Abstract Different types of numerical models exist to describe the non-linear behaviour of reinforced concrete structures. Based on the level of discretization they are often classified as refined or simplified ones. The efficiency of two simplified models using beam elements and damage mechanics in describing the global and local behaviour of lightly reinforced concrete structural walls subjected to seismic loadings is investigated in this paper. The first model uses an implicit and the second an explicit numerical scheme. For each case, the results of the CAMUS 2000 experimental programme are used to validate the approaches. Copyright © 2004 John Wiley & Sons, Ltd. [source] An efficient domain-decomposition pseudo-spectral method for solving elliptic differential equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 10 2008N. Mai-Duy Abstract In this paper, a new numerical scheme based on non-overlapping domain decompositions and integrated Chebyshev approximations for solving elliptic differential equations (DEs) is presented. The distinguishing feature of the present scheme is that it achieves a Cp continuous solution across the interfaces (p is the order of the DE). Several test problems are employed to verify the method. The obtained results indicate that the achievement of higher-order smoothness leads to a significant improvement in accuracy. Copyright © 2007 John Wiley & Sons, Ltd. [source] Extension of weakly compressible approximations to incompressible thermal flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 1 2008Mofdi El-Amrani Abstract Weakly compressible and advection approximations of incompressible isothermal flows were developed and tested in (Commun. Numer. Methods Eng. 2006; 22:831,847). In this paper, we extend the method to solve equations governing incompressible thermal flows. The emphasis is again on the reconstruction of unconditionally stable numerical scheme such that, restriction on time steps, projection procedures, solution of linear system of algebraic equations and staggered grids are completely avoided in its implementation. These features are achieved by combining a low-Mach asymptotic in compressible flow equations with a semi-Lagrangian method for the weakly compressible approach. The time integration is carried out using an explicit Runge,Kutta with variable stages. The method is applied to the natural convection flows in a squared cavity for both steady and transient computations. The numerical results demonstrate high resolution of the proposed method and confirm its capability to provide accurate and efficient simulations for thermal flow problems. Copyright © 2006 John Wiley & Sons, Ltd. [source] Optimal shape of a grain or a fibre cross-section in a two-phase compositeINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 2 2005Vladislav Shenfeld Abstract The shape of grains or of cross-sections of fibres in a two-phase elastic material has an important influence on the overall mechanical behaviour of the composite. In this paper a numerical scheme is devised for determining the optimal shape of a two-dimensional grain or of a fibre's cross-section. The optimization problem is first posed mathematically, using a global objective function, and then solved numerically by the finite element method and a specially designed global optimization scheme. Excellent agreement is obtained with analytical results available for extreme cases. In addition, optimal shapes are obtained under more general conditions. Copyright © 2004 John Wiley & Sons, Ltd. [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] An adaptive multiresolution method for parabolic PDEs with time-step controlINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 6 2009M. O. Domingues Abstract We present an efficient adaptive numerical scheme for parabolic partial differential equations based on a finite volume (FV) discretization with explicit time discretization using embedded Runge,Kutta (RK) schemes. A multiresolution strategy allows local grid refinement while controlling the approximation error in space. The costly fluxes are evaluated on the adaptive grid only. Compact RK methods of second and third order are then used to choose automatically the new time step while controlling the approximation error in time. Non-admissible choices of the time step are avoided by limiting its variation. The implementation of the multiresolution representation uses a dynamic tree data structure, which allows memory compression and CPU time reduction. This new numerical scheme is validated using different classical test problems in one, two and three space dimensions. The gain in memory and CPU time with respect to the FV scheme on a regular grid is reported, which demonstrates the efficiency of the new method. Copyright © 2008 John Wiley & Sons, Ltd. [source] Piecewise constant level set method for structural topology optimizationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 4 2009Peng Wei Abstract In this paper, a piecewise constant level set (PCLS) method is implemented to solve a structural shape and topology optimization problem. In the classical level set method, the geometrical boundary of the structure under optimization is represented by the zero level set of a continuous level set function, e.g. the signed distance function. Instead, in the PCLS approach the boundary is described by discontinuities of PCLS functions. The PCLS method is related to the phase-field methods, and the topology optimization problem is defined as a minimization problem with piecewise constant constraints, without the need of solving the Hamilton,Jacobi equation. The result is not moving the boundaries during the iterative procedure. Thus, it offers some advantages in treating geometries, eliminating the reinitialization and naturally nucleating holes when needed. In the paper, the PCLS method is implemented with the additive operator splitting numerical scheme, and several numerical and procedural issues of the implementation are discussed. Examples of 2D structural topology optimization problem of minimum compliance design are presented, illustrating the effectiveness of the proposed method. Copyright © 2008 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] Improvements and algorithmical considerations on a recent three-dimensional model describing stress-induced solid phase transformationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2002Ferdinando Auricchio Abstract During mechanical loading,unloading cycles shape-memory alloys (SMA) are able to undergo large deformations without showing residual strains (pseudoelasticity) or recovering them through thermal cycles (shape memory effect). Motivated by stress-induced solid phase transformations, these unique behaviours induce the SMA exploitation in innovative and commercially valuable applications, stimulating, consequently, the interest in the development of constitutive models. Also if many models are now available in the literature, effective three-dimensional proposals are still few and limited in several aspects. In this paper, a three-dimensional thermomechanical model recently proposed by Souza et al. (European Journal of Mechanics,A/Solids, 1998; 17: 789,806.) is taken into consideration; such a model is of particular interest for its effectiveness and flexibility, but it also shows some limitations and missing links in the algorithmical counterparts. This work discusses some improvements to the original model as well as the development and the implementation of a robust integration algorithm to be adopted in a numerical scheme, such as a finite-element framework. Copyright © 2002 John Wiley & Sons, Ltd. [source] Simulations of flow through fluid/porous layers by a characteristic-based method on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 11 2001Baili Zhang Abstract An upwind characteristic-based finite volume method on unstructured grids is employed for numerical simulation of incompressible laminar flow and forced convection heat transfer in 2D channels containing simultaneously fluid layers and fluid-saturated porous layers. Hydrodynamic and heat transfer results are reported for two configurations: the first one is a backward-facing step channel with a porous block inserted behind the step, and the second one is a partially porous channel with discrete heat sources on the bottom wall. The effects of Darcy numbers on heat transfer augmentation and pressure loss were investigated for low Reynolds laminar flows. The results demonstrate the accuracy and robustness of the numerical scheme proposed, and suggest that partially porous insertion in a channel can significantly improve heat transfer performance with affordable pressure loss. Copyright © 2001 John Wiley & Sons, Ltd. [source] Numerical simulation of bubble and droplet deformation by a level set approach with surface tension in three dimensionsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 9 2010Roberto Croce Abstract In this paper we present a three-dimensional Navier,Stokes solver for incompressible two-phase flow problems with surface tension and apply the proposed scheme to the simulation of bubble and droplet deformation. One of the main concerns of this study is the impact of surface tension and its discretization on the overall convergence behavior and conservation properties. Our approach employs a standard finite difference/finite volume discretization on uniform Cartesian staggered grids and uses Chorin's projection approach. The free surface between the two fluid phases is tracked with a level set (LS) technique. Here, the interface conditions are implicitly incorporated into the momentum equations by the continuum surface force method. Surface tension is evaluated using a smoothed delta function and a third-order interpolation. The problem of mass conservation for the two phases is treated by a reinitialization of the LS function employing a regularized signum function and a global fixed point iteration. All convective terms are discretized by a WENO scheme of fifth order. Altogether, our approach exhibits a second-order convergence away from the free surface. The discretization of surface tension requires a smoothing scheme near the free surface, which leads to a first-order convergence in the smoothing region. We discuss the details of the proposed numerical scheme and present the results of several numerical experiments concerning mass conservation, convergence of curvature, and the application of our solver to the simulation of two rising bubble problems, one with small and one with large jumps in material parameters, and the simulation of a droplet deformation due to a shear flow in three space dimensions. Furthermore, we compare our three-dimensional results with those of quasi-two-dimensional and two-dimensional simulations. This comparison clearly shows the need for full three-dimensional simulations of droplet and bubble deformation to capture the correct physical behavior. 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] Depth-integrated, non-hydrostatic model for wave breaking and run-upINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2009Yoshiki Yamazaki Abstract This paper describes the formulation, verification, and validation of a depth-integrated, non-hydrostatic model with a semi-implicit, finite difference scheme. The formulation builds on the nonlinear shallow-water equations and utilizes a non-hydrostatic pressure term to describe weakly dispersive waves. A momentum-conserved advection scheme enables modeling of breaking waves without the aid of analytical solutions for bore approximation or empirical equations for energy dissipation. An upwind scheme extrapolates the free-surface elevation instead of the flow depth to provide the flux in the momentum and continuity equations. This greatly improves the model stability, which is essential for computation of energetic breaking waves and run-up. The computed results show very good agreement with laboratory data for wave propagation, transformation, breaking, and run-up. Since the numerical scheme to the momentum and continuity equations remains explicit, the implicit non-hydrostatic solution is directly applicable to existing nonlinear shallow-water models. Copyright © 2008 John Wiley & Sons, Ltd. [source] A higher-order predictor,corrector scheme for two-dimensional advection,diffusion equationINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2008Chuanjian Man Abstract A higher-order accurate numerical scheme is developed to solve the two-dimensional advection,diffusion equation in a staggered-grid system. The first-order spatial derivatives are approximated by the fourth-order accurate finite-difference scheme, thus all truncation errors are kept to a smaller order of magnitude than those of the diffusion terms. Therefore, there is no need to add an artificial diffusion term to balance the unwanted numerical diffusion. For the time derivative, the fourth-order accurate Adams,Bashforth predictor,corrector method is applied. The stability analysis of the proposed scheme is carried out using the Von Neumann method. It is shown that the proposed algorithm has good stability. This method also shows much less spurious oscillations than current lower-order accurate numerical schemes. As a result, the proposed numerical scheme can provide more accurate results for long-time simulations. The proposed numerical scheme is validated against available analytical and numerical solutions for one- and two-dimensional transport problems. One- and two-dimensional numerical examples are presented in this paper to demonstrate the accuracy and conservative properties of the proposed algorithm by comparing with other numerical schemes. The proposed method is demonstrated to be a useful and accurate modelling tool for a wide range of transport problems. Copyright © 2007 John Wiley & Sons, Ltd. [source] Solution of the 2-D shallow water equations with source terms in surface elevation splitting formINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 5 2007Dong-Jun Ma Abstract A vertex-centred finite-volume/finite-element method (FV/FEM) is developed for solving 2-D shallow water equations (SWEs) with source terms written in a surface elevation splitting form, which balances the flux gradients and source terms. The method is implemented on unstructured grids and the numerical scheme is based on a second-order MUSCL-like upwind Godunov FV discretization for inviscid fluxes and a classical Galerkin FE discretization for the viscous gradients and source terms. The main advantages are: (1) the discretization of SWE written in surface elevation splitting form satisfies the exact conservation property (,,-Property) naturally; (2) the simple centred-type discretization can be used for the source terms; (3) the method is suitable for both steady and unsteady shallow water problems; and (4) complex topography can be handled based on unstructured grids. The accuracy of the method was verified for both steady and unsteady problems, including discontinuous cases. The results indicate that the new method is accurate, simple, and robust. Copyright © 2007 John Wiley & Sons, Ltd. [source] LES of the compressed Taylor vortex flow using a finite volume/finite element method on unstructured gridsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006C. Le Ribault Abstract Large-eddy simulations (LES) have been performed of a compressed vortex flow undergoing transition to turbulence. The numerical method is based on a finite volume/finite element discretization of the compressible Navier,Stokes equations on unstructured grids and a Roe second-order scheme with MUSCL extrapolation. A particular attention is paid to the dissipative character of the method, controlled by a coefficient related to the upwind part of the numerical scheme, and its interference with the subgrid model. The accuracy of the method is first checked in the case of decaying homogeneous isotropic turbulence. The investigation is then directed to a plane Taylor vortex flow submitted to compression, in a direction perpendicular to the vorticity vector. This flow is unstable with respect to three-dimensional perturbations and transition to turbulence is observed if the Reynolds number is large enough. The numerical method is used to simulate this vortex flow for two values of the Reynolds number. For the lower value, the flow is unstable but remains laminar and no subgrid model is used. For the higher one, the turbulence appears and the standard and the dynamic Smagorinsky models are tested. The LES results are compared to those obtained by direct numerical simulations (DNS) using a spectral Fourier method. Copyright © 2006 John Wiley & Sons, Ltd. [source] A numerical scheme for strong blast wave driven by explosionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2006Kaori Kato Abstract After the detonation of a solid high explosive, the material has extremely high pressure keeping the solid density and expands rapidly driving strong shock wave. In order to simulate this blast wave, a stable and accurate numerical scheme is required due to large density and pressure changes in time and space. The compressible fluid equations are solved by a fractional step procedure which consists of the advection phase and non-advection phase. The former employs the Rational function CIP scheme in order to preserve monotone signals, and the latter is solved by interpolated differential operator scheme for achieving the accurate calculation. The procedure is categorized into the fractionally stepped semi-Lagrangian. The accuracy of our scheme is confirmed by checking the one-dimensional plane shock tube problem with 103 times initial density and pressure jump in comparison with the analytic solution. The Sedov,Taylor blast wave problem is also examined in the two-dimensional cylindrical coordinate in order to check the spherical symmetry and the convergence rates. Two- and three-dimensional simulations for the blast waves from the explosion in the underground magazine are carried out. It is found that the numerical results show quantitatively good agreement with the experimental data. Copyright © 2006 John Wiley & Sons, Ltd. [source] Extension of an explicit finite volume method to large time steps (CFL>1): application to shallow water flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 1 2006J. Murillo Abstract In this work, the explicit first order upwind scheme is presented under a formalism that enables the extension of the methodology to large time steps. The number of cells in the stencil of the numerical scheme is related to the allowable size of the CFL number for numerical stability. It is shown how to increase both at the same time. The basic idea is proposed for a 1D scalar equation and extended to 1D and 2D non-linear systems with source terms. The importance of the kind of grid used is highlighted and the method is outlined for irregular grids. The good quality of the results is illustrated by means of several examples including shallow water flow test cases. The bed slope source terms are involved in the method through an upwind discretization. Copyright © 2005 John Wiley & Sons, Ltd. [source] 2D thermal/isothermal incompressible viscous flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2005Alfredo Nicolás Abstract 2D thermal and isothermal time-dependent incompressible viscous flows are presented in rectangular domains governed by the Boussinesq approximation and Navier,Stokes equations in the stream function,vorticity formulation. The results are obtained with a simple numerical scheme based on a fixed point iterative process applied to the non-linear elliptic systems that result after a second-order time discretization. The iterative process leads to the solution of uncoupled, well-conditioned, symmetric linear elliptic problems. Thermal and isothermal examples are associated with the unregularized, driven cavity problem and correspond to several aspect ratios of the cavity. Some results are presented as validation examples and others, to the best of our knowledge, are reported for the first time. The parameters involved in the numerical experiments are the Reynolds number Re, the Grashof number Gr and the aspect ratio. All the results shown correspond to steady state flows obtained from the unsteady problem. Copyright © 2005 John Wiley & Sons, Ltd. [source] Numerical analysis of deformed free surface under AC magnetic fieldsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2004Haruhiko Kohno Abstract A novel numerical scheme for the analysis of large deformation of electrically conducting liquid under alternating current magnetic fields is presented. The main features are characterized by two numerical tools; the level set method to calculate deformed free surface stably and the hybrid finite element method and boundary element method to discretize the electromagnetic field efficiently. Two-dimensional numerical simulation of conducting drop deformation is carried out to demonstrate the effectiveness of the present scheme, and the oscillatory behaviour, which depends on the magnitude of surface tension and Lorentz force, is investigated. Copyright © 2004 John Wiley & Sons, Ltd. [source] Godunov-type adaptive grid model of wave,current interaction at cuspate beachesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 6 2004Benedict D. Rogers Abstract This paper presents a second-order accurate Godunov-type numerical scheme for depth- and period-averaged wave,current interaction. A flux Jacobian is derived for the wave conservation equations and its eigensystem determined, enabling Roe's approximate Riemann solver to be used to evaluate convective fluxes. Dynamically adaptive quadtree grids are used to focus on local hydrodynamic features, where sharp gradients occur in the flow variables. Adaptation criteria based on depth-averaged vorticity, wave-height gradient, wave steepness and the magnitude of velocity gradients are found to produce accurate solutions for nearshore circulation at a half-sinusoidal beach. However, the simultaneous combination of two or more separate criteria produces numerical instability and interference unless all criteria are satisfied for mesh depletion. Simulations of wave,current interaction at a multi-cusped beach match laboratory data from the United Kingdom Coastal Research Facility (UKCRF). A parameter study demonstrates the sensitivity of nearshore flow patterns to changes in relative cusp height, angle of wave incidence, bed roughness, offshore wave height and assumed turbulent eddy viscosity. Only a small deviation from normal wave incidence is required to initiate a meandering longshore current. Nearshore circulation patterns are highly dependent on the offshore wave height. Reduction of the assumed eddy viscosity parameter causes the primary circulation cells for normally incident waves to increase in strength whilst producing rip-like currents cutting diagonally across the surf zone. Copyright © 2004 John Wiley & Sons, Ltd. [source] Modelling solitons under the hydrostatic and Boussinesq approximationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003Chris Daily Abstract An examination of solitary waves in 3D, time-dependant hydrostatic and Boussinesq numerical models is presented. It is shown that waves in these models will deform and that only the acceleration term in the vertical momentum equation need be included to correct the wave propagation. Modelling of solitary waves propagating near the surface of a small to medium body of water, such as a lake, are used to illustrate the results. The results are also compared with experiments performed by other authors. Then as an improvement, an alternative numerical scheme is used which includes only the vertical acceleration term. Effects of horizontal and vertical diffusion on soliton wave structure is also discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] An efficient finite difference scheme for free-surface flows in narrow rivers and estuariesINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 3 2003XinJian ChenArticle first published online: 13 MAY 200 Abstract This paper presents a free-surface correction (FSC) method for solving laterally averaged, 2-D momentum and continuity equations. The FSC method is a predictor,corrector scheme, in which an intermediate free surface elevation is first calculated from the vertically integrated continuity equation after an intermediate, longitudinal velocity distribution is determined from the momentum equation. In the finite difference equation for the intermediate velocity, the vertical eddy viscosity term and the bottom- and sidewall friction terms are discretized implicitly, while the pressure gradient term, convection terms, and the horizontal eddy viscosity term are discretized explicitly. The intermediate free surface elevation is then adjusted by solving a FSC equation before the intermediate velocity field is corrected. The finite difference scheme is simple and can be easily implemented in existing laterally averaged 2-D models. It is unconditionally stable with respect to gravitational waves, shear stresses on the bottom and side walls, and the vertical eddy viscosity term. It has been tested and validated with analytical solutions and field data measured in a narrow, riverine estuary in southwest Florida. Model simulations show that this numerical scheme is very efficient and normally can be run with a Courant number larger than 10. It can be used for rivers where the upstream bed elevation is higher than the downstream water surface elevation without any problem. Copyright © 2003 John Wiley & Sons, Ltd. [source] | |||||||||||||||||||