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Surface Integral (surface + integral)

Distribution by Scientific Domains
Engineering60%
Mathematics and Statistics40%

Terms modified by Surface Integral

  • surface integral equation
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    Selected Abstracts

    A viscous vortex particle method for deforming bodies with application to biolocomotion

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2009
    Li Jeany Zhang
    Abstract Bio-inspired mechanics of locomotion generally consist of the interaction of flexible structures with the surrounding fluid to generate propulsive forces. In this work, we extend, for the first time, the viscous vortex particle method (VVPM) to continuously deforming two-dimensional bodies. The VVPM is a high-fidelity Navier,Stokes computational method that captures the fluid motion through evolution of vorticity-bearing computational particles. The kinematics of the deforming body surface are accounted for via a surface integral in the Biot,Savart velocity. The spurious slip velocity in each time step is removed by computing an equivalent vortex sheet and allowing it to flux to adjacent particles; hence, no-slip boundary conditions are enforced. Particles of both uniform and variable size are utilized, and their relative merits are considered. The placement of this method in the larger class of immersed boundary methods is explored. Validation of the method is carried out on the problem of a periodically deforming circular cylinder immersed in a stagnant fluid, for which an analytical solution exists when the deformations are small. We show that the computed vorticity and velocity of this motion are both in excellent agreement with the analytical solution. Finally, we explore the fluid dynamics of a simple fish-like shape undergoing undulatory motion when immersed in a uniform free stream, to demonstrate the application of the method to investigations of biomorphic locomotion. Copyright © 2008 John Wiley & Sons, Ltd. [source]

    Representation of the eigenvalues of the p -Laplacian by means of a surface integral

    MATHEMATISCHE NACHRICHTEN, Issue 11 2005
    Pier Domenico Lamberti
    Abstract We prove a natural generalization to the p -Laplacian of the celebrated Rellich identity. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]

    2D internal flux compatibility equation of the flux Green element method for transient nonlinear potential problems

    NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, Issue 6 2010
    Akpofure E. Taigbenu
    Abstract This article presents the derivation and implementation of the normal directional flux compatibility equation (relationship) at internal nodes when the Green element formulation that consistently provides accurate estimates of the primary variable, and its normal directional derivative (normal flux) is applied in 2D heterogeneous media to steady and transient potential problems. Such a relationship is required to resolve the closure problem due to having fewer integral equations than the number of unknowns at internal nodes. The derivation of the relationship is based on Stokes' theorem, which transforms the contour integral of the normal directional fluxes into a surface integral that is identically zero. The numerical discretization of the compatibility equation is demonstrated with four numerical examples using the six-node quadratic triangular and the four and eight-node rectangular elements. The incorporation of triangular elements into the current formulation demonstrates that the internal compatibility equation can be successfully implemented on irregular grids. The direct calculation of the fluxes significantly enhances the accuracy of the formulation, so that high accuracy, exceeding that of the finite element method, is achieved with very coarse spatial discretization. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010 [source]

    Volumetric methods for evaluating energy loss and heat transfer in cavity flows,

    INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 12 2007
    Stuart Norris
    Abstract Methods have been developed for calculating irreversible energy losses and rates of heat transfer from computational fluid dynamics solutions using volume integrations of energy dissipation or entropy production functions. These methods contrast with the more usual approach of performing first law energy balances over the boundaries of a flow domain. Advantages of the volumetric approach are that the estimates involve the whole flow domain and are hence based on more information than would otherwise be used, and that the energy dissipation or entropy production functions allow for detailed assessment of the mechanisms and regions of energy loss or entropy production. Volume integrations are applied to the calculation of viscous losses in a lid-driven cavity flow, and to the viscous losses and heat transfer due to natural convection in a side-heated cavity. In the convection problem comparison with the entropy increase across a stationary heat conducting layer leads to a novel volume integral expression for the Nusselt number. The predictions using this method compare well with traditional surface integrals and benchmark results. Copyright © 2007 John Wiley & Sons, Ltd. [source]

    Surface integral methods for high-frequency electromagnetic scattering

    PROCEEDINGS IN APPLIED MATHEMATICS & MECHANICS, Issue 1 2007
    M. Ganesh
    Surface integral equation based methods are advantageous for simulation of electromagnetic waves scattered by three dimensional obstacles, because they efficiently reduce the dimension of the problem and are robust for high-frequency problems. However, the cost of setting up the associated discretized dense linear systems is prohibitive due to evaluation of highly oscillatory magnetic and electric dipole surface integral operators using standard cubatures. The computational complexity of evaluating such integrals depends on the incident wave frequency, and the size and shape of the obstacles. In this work we discuss a surface integral reformulation of the scattering problem that involves evaluation of surface integrals with a highly oscillatory physical density, and discuss methods for efficient evaluation of such integrals for a class of smooth three dimensional scatterers whose diameter is a large multiple of the incident wavelength. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) [source]