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Abstract. The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over... more
Abstract. The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over the particle surface plus a pair of singularities ( ...
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We study the two-dimensional potential flow due to a circular cylinder in motion relative to an unbounded fluid. The cylinder consists of a thin, circular porous shell with fluid inside. The full nonlinear hydrodynamic problem is solved... more
We study the two-dimensional potential flow due to a circular cylinder in motion relative to an unbounded fluid. The cylinder consists of a thin, circular porous shell with fluid inside. The full nonlinear hydrodynamic problem is solved by Fourier expansion of Green's theorem. The truncated series is determined numerically by sampling points around the circle. A dimensionless shell parameter is introduced. For homogeneous porous shells, a maximal drag force occurs at the value 0.433 for the shell parameter, but the virtual mass is a monotonous function of the shell parameter. For an inhomogeneous shell, we have found a maximal value for the virtual mass which is 5% above the value for a rigid cylinder. Some of the results may be relevant to offshore engineering, especially in connection with porous coating of platform legs to reduce the total force.
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ABSTRACT
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ABSTRACT
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We propose a node-based local meshless method for advective transport problems that is capable of operating on centrally defined stencils and is suitable for shock-capturing purposes. High spatial convergence rates can be achieved; in... more
We propose a node-based local meshless method for advective transport problems that is capable of operating on centrally defined stencils and is suitable for shock-capturing purposes. High spatial convergence rates can be achieved; in excess of eighth-order in some cases. Strongly-varying smooth profiles may be captured at infinite Péclet number without instability, and for discontinuous profiles the solution exhibits neutrally stable oscillations that can be damped by introducing a small artificial diffusion parameter, allowing a good approximation to the shock-front to be maintained for long travel times without introducing spurious oscillations.The proposed method is based on local collocation with radial basis functions (RBFs) in a “finite collocation” configuration. In this approach the PDE governing and boundary equations are enforced directly within the local RBF collocation systems, rather than being reconstructed from fixed interpolating functions as is typical of finite difference, finite volume or finite element methods. In this way the interpolating basis functions naturally incorporate information from the governing PDE, including the strength and direction of the convective velocity field. By using these PDE-enhanced interpolating functions an “implicit upwinding” effect is achieved, whereby the flow of information naturally respects the specifics of the local convective field. This implicit upwinding effect allows high-convergence solutions to be obtained on centred stencils for advection problems.The method is formulated using a high-convergence implicit timestepping algorithm based on Richardson extrapolation. The spatial and temporal convergence of the proposed approach is demonstrated using smooth functions with large gradients. The capture of discontinuities is then investigated, showing how the addition of a dynamic stabilisation parameter can damp the neutrally stable oscillations with limited smearing of the shock front.
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... Clemente Cobos Sánchez a , E-mail The Corresponding Author , Henry Power b , Corresponding Author Contact Information , E-mail The Corresponding Author , Salvador G. Garcia a , E-mail The Corresponding Author and Amelia Rubio Bretones... more
... Clemente Cobos Sánchez a , E-mail The Corresponding Author , Henry Power b , Corresponding Author Contact Information , E-mail The Corresponding Author , Salvador G. Garcia a , E-mail The Corresponding Author and Amelia Rubio Bretones a , E-mail The Corresponding ...
Research Interests: Mechanical Engineering, Civil Engineering, Applied Mathematics, MRI, Inverse Problems, and 14 moreMagnetic field, Safety, Gradient, Boundary Element Method, Volume, Electric Fields, Inverse Problem, Head, Magnetic Fields, Multi Domain, Electric Currents, Human Subjects, Electric Field, and Domain Decomposition
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Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs).... more
Problems involving nonlinear time-dependent heat conduction in materials which have temperature-dependent thermal properties are solved with a novel meshless numerical solution technique using multiquadric radial basis functions (RBFs). Unlike traditional RBF collocation methods, the local Hermitian interpolation (LHI) method examined here can be scaled to arbitrarily large problems without numerical ill-conditioning or computational cost issues, due to the presence of small overlapping interpolation systems which grow in number but not in size as the global dataset grows. The flexibility of the full-domain multiquadric collocation method to directly interpolate arbitrary boundary conditions is maintained, via the local interpolations.The Kirchhoff transformation is employed to reduce the degree of nonlinearity in the governing PDE, and a high-resolution interpolation procedure is outlined to transform the various thermal properties to Kirchhoff-space. The implementation procedure i...
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This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non-Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non-linear... more
This paper presents a boundary element method (BEM) based on a subdomain approach for the solution of non-Newtonian fluid flow problems which include thermal effects and viscous dissipation. The volume integral arising from non-linear terms is converted into equivalent boundary integrals by the multi-domain dual reciprocity method (MD-DRM) in each subdomain. Augmented thin plate splines interpolation functions are used for
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ABSTRACT The effect of solid particles within flows having zones of recirculation is of interest in pulverised fuel distribution and combustion at burners. Previous modelling of a 1/4 scale test rig was performed by Giddings et al.... more
ABSTRACT The effect of solid particles within flows having zones of recirculation is of interest in pulverised fuel distribution and combustion at burners. Previous modelling of a 1/4 scale test rig was performed by Giddings et al. (2004), and an instability was later identified within the domain. Subsequently the transient dynamics of the flow of air through a double expansion were investigated numerically and a recirculation zone was found to develop at one of the four corners of the expansion. In the work presented here the flow of solid particles through this double expansion is investigated using the commercial software ANSYS FLUENT R14.0. The Stress-Omega Reynolds Stress Model is used to model the gas phase turbulence and the Discrete Particle Model is used to model the solid particle flow. The dynamics of the flow are reported here for 10 pm and 60 pm particles and for mass loadings from 0 to 1 kg(particles)/kg(air). The simulations show a distinct transition to a vortex shedding type instability with the addition of the discrete phase. Furthermore, for increasing mass loading and particle Stokes number the Coanda effect is reduced leading to two large recirculation zones in opposing corners of the domain. The characteristics of the flow field are in qualitative agreement with studies of particle flows in jet flows and shear layers. This work serves to highlight some of the challenges in modelling complex pneumatic conveying flows from an industrial perspective. (C) 2014 The Authors. Published by Elsevier B.V.
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partially or totally submerged body of arbitrary shape moving with constant speed is analyzed using Oseen's approximate equation for viscous incompressible fluids. This Analysis is based upon the derivation of integral... more
partially or totally submerged body of arbitrary shape moving with constant speed is analyzed using Oseen's approximate equation for viscous incompressible fluids. This Analysis is based upon the derivation of integral identities of Green's type, and identification of surface hydrodynamic pote~ tlala completely analogous to the classical single and double-layer potentials already found for Laplace's equation, heat equation, Stokes flow
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Abstract. The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over... more
Abstract. The problem of determining the slow viscous flow of an unbounded fluid past a single solid particle is formulated exactly as a system of linear Fredholm integral equations of the second kind for a distribution of Stresslets over the particle surface plus a pair of singularities ( ...
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Research Interests: Power Electronics and IEE
The numerical simulation of microfluid flow through the solution of governing equations based on continuum models has to be done under the consideration of appropriate slip boundary conditions to account for the velocity jump at the... more
The numerical simulation of microfluid flow through the solution of governing equations based on continuum models has to be done under the consideration of appropriate slip boundary conditions to account for the velocity jump at the solid-fluid interface. The linear model proposed by Navier states a relation between the tangential shear rate and the fluid-wall velocity differences and has been
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ABSTRACT We study the two-dimensional potential flow due to a circular cylinder in motion relative to an unbounded fluid. The cylinder consists of a thin, circular porous shell with fluid inside. The full nonlinear hydrodynamic problem is... more
ABSTRACT We study the two-dimensional potential flow due to a circular cylinder in motion relative to an unbounded fluid. The cylinder consists of a thin, circular porous shell with fluid inside. The full nonlinear hydrodynamic problem is solved by Fourier expansion of Green''s theorem. The truncated series is determined numerically by sampling points around the circle. A dimensionless shell parameter is introduced. For homogeneous porous shells, a maximal drag force occurs at the value 0.433 for the shell parameter, but the virtual mass is a monotonous function of the shell parameter. For an inhomogeneous shell, we have found a maximal value for the virtual mass which is 5% above the value for a rigid cylinder. Some of the results may be relevant to offshore engineering, especially in connection with porous coating of platform legs to reduce the total force.
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Ooms et al. (1985) studied the propagation of long waves of finite amplitude at the interface of two superposed layers of fluid of different viscosities between two horizontal plates. They simplified the Navier-Stokes equations by using a... more
Ooms et al. (1985) studied the propagation of long waves of finite amplitude at the interface of two superposed layers of fluid of different viscosities between two horizontal plates. They simplified the Navier-Stokes equations by using a perturbation calculation with the ratio of the ...
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Atmospheric lead levels were examined to assess the consequences of the 46 percent reduction in the lead content of premium grade petrol in New Zealand. Since this change was implemented in July 1986 observed levels of atmospheric lead... more
Atmospheric lead levels were examined to assess the consequences of the 46 percent reduction in the lead content of premium grade petrol in New Zealand. Since this change was implemented in July 1986 observed levels of atmospheric lead decreased by 38 percent, but all or part of this reduction may have been due to factors other than fluctuations in lead
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Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by... more
Boundary element methods represent a valuable approach for designing gradient coils; these methods are based on meshing the current carrying surface into an array of boundary elements. The temporally varying magnetic fields produced by gradient coils induce electric currents in conducting tissues and so the exposure of human subjects to these magnetic fields has become a safety concern, especially with the increase in the strength of the field gradients used in magnetic resonance imaging. Here we present a boundary element method for the design of coils that minimize the electric field induced in prescribed conducting systems. This work also details some numerical examples of the application of this coil design method. The reduction of the electric field induced in a prescribed region inside the coils is also evaluated.
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ABSTRACT This work is concerned with the analysis of the effect of precipitation inhibitors on the growth of crystals from over-saturated solutions, by the numerical simulation of the fundamental mechanisms of such crystallization... more
ABSTRACT This work is concerned with the analysis of the effect of precipitation inhibitors on the growth of crystals from over-saturated solutions, by the numerical simulation of the fundamental mechanisms of such crystallization process. The complete crystallization process in the presence of precipitation inhibitor is defined by a set of coupled partial differential equations that needs to be solved in a recursive manner, due to the inhibitor modification of the molar flux of the mineral at the crystal interface. This set of governing equations needs to satisfy the corresponding initial and boundary conditions of the problem where it is necessary to consider the additional unknown of a moving interface, i.e., the growing crystal surface. For the numerical solution of the proposed problem, we used a truly meshless numerical scheme based upon Hermite interpolation property of the radial basis functions. The use of a Hermitian meshless collocation numerical approach was selected in this work due to its flexibility on dealing with moving boundary problems and their high accuracy on predicting surface fluxes, which is a crucial part of the diffusion controlled crystallization process considered here. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006
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This chapter presents direct formulations of the boundary element method for the two-dimensional scattering of seismic waves from irregular topographies and buried valleys. The BEM models were formulated with isoparametric, quadratic... more
This chapter presents direct formulations of the boundary element method for the two-dimensional scattering of seismic waves from irregular topographies and buried valleys. The BEM models were formulated with isoparametric, quadratic boundary elements, and were employed to simulate a section of the Mexico City valley. Because the Mexico City valley is relatively flat and shallow, and the contrast of S waves between the clays and the basement rock is very high, it is believed that the one-dimensional theory is sufficient to explain the amplification patterns. Although this is true for many sites, results from accelerometric data suggest that two-and three-dimensional models are needed to explain the amplification behaviour at other sites, particularly near the borders of the valley.
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"A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial... more
"A meshless numerical scheme is developed for solving a generic version of the non-linear convection-diffusion-reaction equation in two-dim-ensional domains. The Local Hermitian Interpolation (LHI) method is employed for the spatial discretization and several strategies are implemented for the solution of the resulting non-linear equation system, among them the Picard iteration, the Newton Raphson method and a truncated version of the Homotopy Analysis Method (HAM). The LHI method is a local collocation strategy in which Radial Basis Functions (RBFs) are employed to build the interpolation function. Unlike the original Kansa’s Method, the LHI is applied locally and the boundary and governing equation differential operators are used to obtain the interpolation function, giving a symmetric and non-singular collocation matrix. Analytical and Numerical Jacobian matrices are tested for the Newton-Raphson method and the derivatives of the governing equation with respect to the homotopy parameter are obtained analytically. The numerical scheme is verified by comparing the obtained results to the one-dimensional Burgers’ and two-dimensional Richards’ analytical solutions. The same results are obtained for all the non-linear solvers tested, but better convergence rates are attained with the Newton Raphson method in a double iteration scheme."