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Conservation Properties (conservation + property)
Selected AbstractsConservation properties of a time FE method.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 13 2005Part IV: Higher order energy, momentum conserving schemes Abstract In the present paper a systematic development of higher order accurate time stepping schemes which exactly conserve total energy as well as momentum maps of underlying finite-dimensional Hamiltonian systems with symmetry is shown. The result of this development is the enhanced Galerkin (eG) finite element method in time. The conservation of the eG method is generally related to its collocation property. Total energy conservation, in particular, is obtained by a new projection technique. The eG method is, moreover, based on objective time discretization of the used strain measure. This paper is concerned with particle dynamics and semi-discrete non-linear elastodynamics. The related numerical examples show good performance in presence of stiffness as well as for calculating large-strain motions. Copyright © 2005 John Wiley & Sons, Ltd. [source] A linearized implicit pseudo-spectral method for some model equations: the regularized long wave equationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 11 2003K. Djidjeli Abstract An efficient numerical method is developed for the numerical solution of non-linear wave equations typified by the regularized long wave equation (RLW) and its generalization (GRLW). The method developed uses a pseudo-spectral (Fourier transform) treatment of the space dependence together with a linearized implicit scheme in time. =10pt An important advantage to be gained from the use of this method, is the ability to vary the mesh length, thereby reducing the computational time. Using a linearized stability analysis, it is shown that the proposed method is unconditionally stable. The method is second order in time and all-order in space. The method presented here is for the RLW equation and its generalized form, but it can be implemented to a broad class of non-linear long wave equations (Equation (2)), with obvious changes in the various formulae. Test problems, including the simulation of a single soliton and interaction of solitary waves, are used to validate the method, which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. Copyright © 2003 John Wiley & Sons, Ltd. [source] Some further properties of the superconvergent flux projectionINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 4 2002Graham F. Carey Abstract Some properties of the integral superconvergent flux (post-processing) projection formula are investigated: (1) A Green,Gauss formula together with the partition of unity property of the finite element basis imply global and local conservation properties and a local flux or stress recovery strategy; (2) The equivalence to a Lagrange multiplier mixed formulation is used to interpret the associated consistency requirement on the flux expansion via an inf,sup or LBB condition and (3) The resulting conditions on the flux basis are examined and the presence of oscillatory modes demonstrated. Copyright © 2002 John Wiley & Sons, Ltd. [source] Parallel asynchronous variational integratorsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 3 2007Kedar G. Kale Abstract This paper presents a scalable parallel variational time integration algorithm for nonlinear elastodynamics with the distinguishing feature of allowing each element in the mesh to have a possibly different time step. Furthermore, the algorithm is obtained from a discrete variational principle, and hence it is termed parallel asynchronous variational integrator (PAVI). The underlying variational structure grants it outstanding conservation properties. Based on a domain decomposition strategy, PAVI combines a careful scheduling of computations with fully asynchronous communications to provide a very efficient methodology for finite element models with even mild distributions of time step sizes. Numerical tests are shown to illustrate PAVI's performance on both slow and fast networks, showing scalability properties similar to the best parallel explicit synchronous algorithms, with lower execution time. Finally, a numerical example in which PAVI needs ,100 times less computing than an explicit synchronous algorithm is shown. Copyright © 2006 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] A staggered conservative scheme for every Froude number in rapidly varied shallow water flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2003G. S. Stelling Professor Abstract This paper proposes a numerical technique that in essence is based upon the classical staggered grids and implicit numerical integration schemes, but that can be applied to problems that include rapidly varied flows as well. Rapidly varied flows occur, for instance, in hydraulic jumps and bores. Inundation of dry land implies sudden flow transitions due to obstacles such as road banks. Near such transitions the grid resolution is often low compared to the gradients of the bathymetry. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. The scheme described here, combines the efficiency of staggered grids with conservation properties so as to ensure accurate results for rapidly varied flows, as well as in expansions as in contractions. In flow expansions, a numerical approximation is applied that is consistent with the momentum principle. In flow contractions, a numerical approximation is applied that is consistent with the Bernoulli equation. Both approximations are consistent with the shallow water equations, so under sufficiently smooth conditions they converge to the same solution. The resulting method is very efficient for the simulation of large-scale inundations. Copyright © 2003 John Wiley & Sons, Ltd. [source] Metabolic response to two hydrocooling temperatures in sweet cherries cv Lapins and cv SunburstJOURNAL OF THE SCIENCE OF FOOD AND AGRICULTURE, Issue 12 2006Rafael Alique Abstract Physiological and metabolic characterisation and analysis of response to two hydrocooling temperatures in cv Sunburst (early season) and cv Lapins (mid-season) cherries during post-harvest life has been studied. Samples were hydrocooled with water at 1 °C to reach 6 °C inside the fruit (HC-6C) and 2 °C (HC-2C) inside the fruit. After harvesting, Sunburst samples presented higher respiration rates and lower malic acid and sorbitol contents than Lapins. Glucose and fructose contents were similar in the two varieties. Sunburst control exhibited a higher respiration rate than Lapins and a higher rate of conversion from sorbitol to fructose. The change of glucose and malic acid consumption over 4 days at 20 °C was similar for the two varieties. Hydrocooling reduced respiration and the consumption of respiratory substrates. The residual effect of hydrocooling was especially significant in cherries of both varieties that had been pre-cooled to 2 °C. Hydrocooling delayed loss of skin and pulp firmness, and reduced loss of titratable acid and soluble solid contents over 4 days at 20 °C in both varieties. Hydrocooling to 2 °C checked loss of quality with respect to controls for both varieties after 4 days at 20 °C. Lapins showed better conservation properties than Sunburst under all the experimental storage conditions. Hydrocooling reduced total losses in both varieties, especially in cherries pre-cooled to 2 °C. Hydrocooling also had several residual effects: reduction of the respiration rate and consumption of respiratory substrates, and slowing of loss of quality, particularly for Lapins. Copyright © 2006 Society of Chemical Industry [source] An enhanced-physics-based scheme for the NS-, turbulence modelNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2010William W. Miles Abstract We study a new enhanced-physics-based numerical scheme for the NS-alpha turbulence model that conserves both energy and helicity. Although most turbulence models (in the continuous case) conserve only energy, NS-alpha is one of only a very few that also conserve helicity. This is one reason why it is becoming accepted as the most physically accurate turbulence model. However, no numerical scheme for NS-alpha, until now, conserved both energy and helicity, and thus the advantage gained in physical accuracy by modeling with NS-alpha could be lost in a computation. This report presents a finite element numerical scheme, and gives a rigorous analysis of its conservation properties, stability, solution existence, and convergence. A key feature of the analysis is the identification of the discrete energy and energy dissipation norms, and proofs that these norms are equivalent (provided a careful choice of filtering radius) in the discrete space to the usual energy and energy dissipation norms. Numerical experiments are given to demonstrate the effectiveness of the scheme over usual (helicity-ignoring) schemes. A generalization of this scheme to a family of high-order NS-alpha-deconvolution models, which combine the attractive physical properties of NS-alpha with the high accuracy gained by combining ,-filtering with van Cittert approximate deconvolution. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] A meshless method using the radial basis functions for numerical solution of the regularized long wave equationNUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 4 2010Ali Shokri Abstract This article discusses on the solution of the regularized long wave (RLW) equation, which is introduced to describe the development of the undular bore, has been used for modeling in many branches of science and engineering. A numerical method is presented to solve the RLW equation. The main idea behind this numerical simulation is to use the collocation and approximating the solution by radial basis functions (RBFs). To avoid solving the nonlinear system, a predictor-corrector scheme is proposed. Several test problems are given to validate the new technique. The numerical simulation, includes the propagation of a solitary wave, interaction of two positive solitary waves, interaction of a positive and a negative solitary wave, the evaluation of Maxwellian pulse into stable solitary waves and the development of an undular bore. The three invariants of the motion are calculated to determine the conservation properties of the algorithm. The results of numerical experiments are compared with analytical solution and with those of other recently published methods to confirm the accuracy and efficiency of the presented scheme.© 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source] Spectroscopic study of the physical properties making trehalose a stabilizing and shelf life extending compound in food industryQUALITY ASSURANCE & SAFETY OF CROPS & FOOD, Issue 2 2010S. Magazù Abstract Introduction Trehalose, a glass-forming bioprotectant disaccharide, has been demonstrated to possess significant potential within the food industry. It does not interact with reactive molecules such as amino groups from peptides and proteins, preventing the degradation and aggregation due to Maillard reactions. Objective This paper aims to review at the molecular level the effects of trehalose on the structural and dynamical properties of water and on protein to highlight the stabilization and conservation properties on food products. Results and Conclusions The experimental findings presented show that water molecules are arranged in presence of trehalose in a particular configuration which avoids ice formation, so limiting damage due to freezing and cooling. On the other hand, homologous disaccharides, and trehalose to a greater extent, slow down the dynamics of water with a significant influence on the biological activity. These results imply that trehalose has a greater ability to bind volatile substances and deliver superior bioprotective effectiveness. Furthermore trehalose is shown to be incapable of taking part in the denaturation process of lysozyme under thermal stress. [source] Towards a consistent numerical compressible non-hydrostatic model using generalized Hamiltonian toolsTHE QUARTERLY JOURNAL OF THE ROYAL METEOROLOGICAL SOCIETY, Issue 635 2008Almut Gassmann Abstract A set of compressible non-hydrostatic equations for a turbulence-averaged model atmosphere comprising dry air and water in three phases plus precipitating fluxes is presented, in which common approximations are introduced in such a way that no inconsistencies occur in the associated budget equations for energy, mass and Ertel's potential vorticity. These conservation properties are a prerequisite for any climate simulation or NWP model. It is shown that a Poisson bracket form for the ideal fluid part of the full-physics equation set can be found, while turbulent friction and diabatic heating are added as separate ,dissipative' terms. This Poisson bracket is represented as a sum of a two-fold antisymmetric triple bracket (a Nambu bracket represented as helicity bracket) plus two antisymmetric brackets (so-called mass and thermodynamic brackets of the Poisson type). The advantage of this approach is that the given conservation properties and the structure of the brackets provide a good strategy for the construction of their discrete analogues. It is shown how discrete brackets are constructed to retain their antisymmetric properties throughout the spatial discretisation process, and a method is demonstrated how the time scheme can also be incorporated in this philosophy. Copyright © 2008 Royal Meteorological Society [source] On the design of energy,momentum integration schemes for arbitrary continuum formulations.INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 15 2004Applications to classical, chaotic motion of shells Abstract The construction of energy,momentum methods depends heavily on three kinds of non-linearities: (1) the geometric (non-linearity of the strain,displacement relation), (2) the material (non-linearity of the elastic constitutive law), and (3) the one exhibited in displacement-dependent loading. In previous works, the authors have developed a general method which is valid for any kind of geometric non-linearity. In this paper, we extend the method and combine it with a treatment of material non-linearity as well as that exhibited in force terms. In addition, the dynamical formulation is presented in a general finite element framework where enhanced strains are incorporated as well. The non-linearity of the constitutive law necessitates a new treatment of the enhanced strains in order to retain the energy conservation property. Use is made of the logarithmic strain tensor which allows for a highly non-linear material law, while preserving the advantage of considering non-linear vibrations of classical metallic structures. Various examples and applications to classical and non-classical vibrations and non-linear motion of shells are presented, including (1) chaotic motion of arches, cylinders and caps using a linear constitutive law and (2) large overall motion and non-linear vibration of shells using non-linear constitutive law. Copyright © 2004 John Wiley & Sons, Ltd. [source] A volume-of-fluid method for incompressible free surface flowsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009I. R. Park Abstract This paper proposes a hybrid volume-of-fluid (VOF) level-set method for simulating incompressible two-phase flows. Motion of the free surface is represented by a VOF algorithm that uses high resolution differencing schemes to algebraically preserve both the sharpness of interface and the boundedness of volume fraction. The VOF method is specifically based on a simple order high resolution scheme lower than that of a comparable method, but still leading to a nearly equivalent order of accuracy. Retaining the mass conservation property, the hybrid algorithm couples the proposed VOF method with a level-set distancing algorithm in an implicit manner when the normal and the curvature of the interface need to be accurate for consideration of surface tension. For practical purposes, it is developed to be efficiently and easily extensible to three-dimensional applications with a minor implementation complexity. The accuracy and convergence properties of the method are verified through a wide range of tests: advection of rigid interfaces of different shapes, a three-dimensional air bubble's rising in viscous liquids, a two-dimensional dam-break, and a three-dimensional dam-break over an obstacle mounted on the bottom of a tank. The standard advection tests show that the volume advection algorithm is comparable in accuracy with geometric interface reconstruction algorithms of higher accuracy than other interface capturing-based methods found in the literature. The numerical results for the remainder of tests show a good agreement with other numerical solutions or available experimental data. Copyright © 2009 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] A semi-Lagrangian level set method for incompressible Navier,Stokes equations with free surfaceINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2005Leo Miguel González Gutiérrez Abstract In this paper, we formulate a level set method in the framework of finite elements-semi-Lagrangian methods to compute the solution of the incompressible Navier,Stokes equations with free surface. In our formulation, we use a quasi-monotone semi-Lagrangian scheme, which is both unconditionally stable and essentially non oscillatory, to compute the advective terms in the Navier,Stokes equations, the transport equation and the equation of the reinitialization stage for the level set function. The method we propose is quite robust and flexible with regard to the mesh and the geometry of the domain, as well as the magnitude of the Reynolds number. We illustrate the performance of the method in several examples, which range from a benchmark problem to test the volume conservation property of the method to the flow past a NACA0012 foil at high Reynolds number. Copyright © 2005 John Wiley & Sons, Ltd. [source] Superconvergence and H(div) projection for discontinuous Galerkin methodsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 10 2003Peter Bastian Abstract We introduce and analyse a projection of the discontinuous Galerkin (DG) velocity approximations that preserve the local mass conservation property. The projected velocities have the additional property of continuous normal component. Both theoretical and numerical convergence rates are obtained which show that the accuracy of the DG velocity field is maintained. Superconvergence properties of the DG methods are shown. Finally, numerical simulations of complicated flow and transport problem illustrate the benefits of the projection. 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