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Touvia Miloh - One of the best experts on this subject based on the ideXlab platform.

  • Radiation and oblique Diffraction by submerged prolate spheroids in water of finite depth
    Journal of Ocean Engineering and Marine Energy, 2015
    Co-Authors: Ioannis K. Chatjigeorgiou, Touvia Miloh
    Abstract:

    In the present study we present a general methodology for estimating the hydrodynamic (added-mass and damping) coefficients of a fully submerged (below a free-surface) elongated axisymmetric ocean-going body (approximated by a prolate spheroid) in water of finite depth (rigid even sea bottom). Using the same approach, we also provide a solution for the corresponding linearized Diffraction Problem and analytically determine the exciting hydrodynamic forces and moments exerted on the body due to obliquely incident monochromatic surface waves. A comprehensive series of numerical simulations is presented for the relevant hydrodynamic parameters depending on the wave encounter frequency and angle of incidence, including body submergence and slenderness-ratio as well as the water depth. Numerical validations are also provided as limiting cases for spherical shapes in finite water and for spheroidal geometries in water of infinite depth.

  • hydrodynamics of submerged prolate spheroids advancing under waves wave Diffraction with forward speed
    Journal of Fluids and Structures, 2014
    Co-Authors: Ioannis K. Chatjigeorgiou, Touvia Miloh
    Abstract:

    Abstract The present study treats the hydrodynamic Diffraction Problem including forward speed of a fully submerged prolate spheroid advancing rectilinearly under a monochromatic wave field in water of infinite depth. The analytic method explicitly satisfies the Kelvin–Neumann boundary conditions. The formulation is based on employing spheroidal harmonics and expressing the ultimate image singularity system as a series of multipoles distributed along the major axis of the spheroid between the two foci. The outlined procedure results in compact closed-form expressions for the six Kirchhoff velocity potentials as well as for the various components of the hydrodynamic loads exerted on the rigid body moving under waves.

Thomas Wick - One of the best experts on this subject based on the ideXlab platform.

  • iterative coupling of flow geomechanics and adaptive phase field fracture including level set crack width approaches
    Journal of Computational and Applied Mathematics, 2017
    Co-Authors: Mary F Wheeler, Thomas Wick
    Abstract:

    In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fracture permeability into the pressure Diffraction Problem which is crucial for fluid filled fractures. Our developments are substantiated with several numerical tests that include comparisons of computational cost for iterative coupling and nonlinear and linear iterations as well as convergence studies in space and time. Fixed-stress formulations for fluid-filled phase-field fractures.Accurate fracture-width finite element computations using level-sets.Numerical examples in 2D and 3D with spatial and temporal convergence studies.

  • iterative coupling of flow geomechanics and adaptive phase field fracture including level set crack width approaches
    arXiv: Numerical Analysis, 2016
    Co-Authors: Sanghyun Lee, Thomas Wick, Mary F Wheeler
    Abstract:

    In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fracture permeability into the pressure Diffraction Problem which is crucial for fluid filled fractures. Our developments are substantiated with several numerical tests that include comparisons of computational cost for iterative coupling and nonlinear and linear iterations as well as convergence studies in space and time.

  • a phase field method for propagating fluid filled fractures coupled to a surrounding porous medium
    Multiscale Modeling & Simulation, 2015
    Co-Authors: Andro Mikelic, Mary F Wheeler, Thomas Wick
    Abstract:

    The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and nonplanar propagation in possibly heterogeneous media. In this paper, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic Diffraction Problem. Here, the phase-field variable is used as an indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase field, pressure) is a multiscale Problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in two and three dimensions.

Mary F Wheeler - One of the best experts on this subject based on the ideXlab platform.

  • iterative coupling of flow geomechanics and adaptive phase field fracture including level set crack width approaches
    Journal of Computational and Applied Mathematics, 2017
    Co-Authors: Mary F Wheeler, Thomas Wick
    Abstract:

    In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fracture permeability into the pressure Diffraction Problem which is crucial for fluid filled fractures. Our developments are substantiated with several numerical tests that include comparisons of computational cost for iterative coupling and nonlinear and linear iterations as well as convergence studies in space and time. Fixed-stress formulations for fluid-filled phase-field fractures.Accurate fracture-width finite element computations using level-sets.Numerical examples in 2D and 3D with spatial and temporal convergence studies.

  • iterative coupling of flow geomechanics and adaptive phase field fracture including level set crack width approaches
    arXiv: Numerical Analysis, 2016
    Co-Authors: Sanghyun Lee, Thomas Wick, Mary F Wheeler
    Abstract:

    In this work, we present numerical studies of fixed-stress iterative coupling for solving flow and geomechanics with propagating fractures in a porous medium. Specifically, fracture propagations are described by employing a phase-field approach. The extension to fixed-stress splitting to propagating phase-field fractures and systematic investigation of its properties are important enhancements to existing studies. Moreover, we provide an accurate computation of the fracture opening using level-set approaches and a subsequent finite element interpolation of the width. The latter enters as fracture permeability into the pressure Diffraction Problem which is crucial for fluid filled fractures. Our developments are substantiated with several numerical tests that include comparisons of computational cost for iterative coupling and nonlinear and linear iterations as well as convergence studies in space and time.

  • a phase field method for propagating fluid filled fractures coupled to a surrounding porous medium
    Multiscale Modeling & Simulation, 2015
    Co-Authors: Andro Mikelic, Mary F Wheeler, Thomas Wick
    Abstract:

    The recently introduced phase-field approach for pressurized fractures in a porous medium offers various attractive computational features for numerical simulations of cracks such as joining, branching, and nonplanar propagation in possibly heterogeneous media. In this paper, the pressurized phase-field framework is extended to fluid-filled fractures in which the pressure is computed from a generalized parabolic Diffraction Problem. Here, the phase-field variable is used as an indicator function to combine reservoir and fracture pressure. The resulting three-field framework (elasticity, phase field, pressure) is a multiscale Problem that is based on the Biot equations. The proposed numerical solution algorithm iteratively decouples the equations using a fixed-stress splitting. The framework is substantiated with several numerical benchmark tests in two and three dimensions.

Ioannis K. Chatjigeorgiou - One of the best experts on this subject based on the ideXlab platform.

  • Radiation and oblique Diffraction by submerged prolate spheroids in water of finite depth
    Journal of Ocean Engineering and Marine Energy, 2015
    Co-Authors: Ioannis K. Chatjigeorgiou, Touvia Miloh
    Abstract:

    In the present study we present a general methodology for estimating the hydrodynamic (added-mass and damping) coefficients of a fully submerged (below a free-surface) elongated axisymmetric ocean-going body (approximated by a prolate spheroid) in water of finite depth (rigid even sea bottom). Using the same approach, we also provide a solution for the corresponding linearized Diffraction Problem and analytically determine the exciting hydrodynamic forces and moments exerted on the body due to obliquely incident monochromatic surface waves. A comprehensive series of numerical simulations is presented for the relevant hydrodynamic parameters depending on the wave encounter frequency and angle of incidence, including body submergence and slenderness-ratio as well as the water depth. Numerical validations are also provided as limiting cases for spherical shapes in finite water and for spheroidal geometries in water of infinite depth.

  • hydrodynamics of submerged prolate spheroids advancing under waves wave Diffraction with forward speed
    Journal of Fluids and Structures, 2014
    Co-Authors: Ioannis K. Chatjigeorgiou, Touvia Miloh
    Abstract:

    Abstract The present study treats the hydrodynamic Diffraction Problem including forward speed of a fully submerged prolate spheroid advancing rectilinearly under a monochromatic wave field in water of infinite depth. The analytic method explicitly satisfies the Kelvin–Neumann boundary conditions. The formulation is based on employing spheroidal harmonics and expressing the ultimate image singularity system as a series of multipoles distributed along the major axis of the spheroid between the two foci. The outlined procedure results in compact closed-form expressions for the six Kirchhoff velocity potentials as well as for the various components of the hydrodynamic loads exerted on the rigid body moving under waves.

  • Hydrodynamic exciting forces on a submerged oblate spheroid in regular waves
    Computers & Fluids, 2012
    Co-Authors: Ioannis K. Chatjigeorgiou
    Abstract:

    Abstract It is the purpose of this study to provide the analytic solution for the hydrodynamic Diffraction Problem by stationary, submerged oblate spheroidal bodies subjected to harmonic incident waves in deep water. The analytical process employs the multipole expansion terms derived by Thorne [1] which describe the velocity potential at singular points within a fluid domain with free upper surface and infinite water depth. The multipole potentials are used to analytically formulate the Diffraction component of the velocity potential which is initially described by relations involving both spherical and polar coordinates. The goal is to transform the constituent terms of the multipole potentials as well as the incident wave component in oblate spheroidal coordinates. To this end, the appropriate addition theorems are derived which recast Thorne’s [1] formulas into infinite series of associated Legendre functions.

Pleshchinskii N. - One of the best experts on this subject based on the ideXlab platform.

  • Analysis of electromagnetic wave propagation through a layer with graded-index distribution of refraction index
    2020
    Co-Authors: Pleshchinskii N., Tumakov D.
    Abstract:

    The Problem of plane electromagnetic harmonic wave Diffraction on a graded-refractive-index layer of some thickness is considered. It is assumed that refractive index of a layer monotonically increases and then monotonically decreases. Cases of the linear, parabolic, sinusoidal, exponential and logarithmic refractive index profiles of the layer are investigated. The Diffraction Problem is reduced to an ordinary differential equation with appropriate boundary conditions. The Problem for the linear profile is solved analytically; for the other profiles it is investigated numerically. The method of approximating an integral identity is applied to increase accuracy of the grid solution of the boundary value Problem. Emphasis is given to the cases, in which wave energy, either reflected or transited, reaches maxima

  • Parallel algorithm of solving the electromagnetic wave Diffraction Problem on the spherical screen
    2020
    Co-Authors: Karchevskiy E., Pleshchinskii N.
    Abstract:

    The electromagnetic wave Diffraction Problem on a thin conducting spherical screen is reduced to pair summatorial equation relative to unknown coefficients of expansion into a series of spherical waves. This equation can be transformed to a regular infinite set of linear algebraic equations by integral-summatorial identities method. For all stages of numerical algorithm of solving the Problem the parallel calculating processes are possible. At first, if field traces of outside source at the sphere are decomposed onto magnetic and electric parts, then magnetic and electric parts of the unknown field can be found independently. Secondly, if coefficients of field conjugation conditions at the sphere do not depend on longitude coordinate, then calculations also can be fulfilled independently for every number of the series coefficients. Thirdly, if by reduction of infinite set the finite set of linear equations of large dimension is obtained, then it can be solved by one of parallel algorithms. But the most effect can be obtained just at the stage of calculating the auxiliary integrals over screen

  • On Problems of electromagnetic wave Diffraction on periodical sets of heterogeneities in the layered media
    2020
    Co-Authors: Osipov E., Pleshchinskii N., Rogozhin P.
    Abstract:

    The universal approach to solving the Diffraction Problems on the periodical set of heterogeneities in the layered media is proposed. The infinite periodic grating consisting of thin conducting bands embedded into a dielectric plate is considered as an example. At first, it is advisable to solve the auxiliary Diffraction Problem in the case when the heterogeneities are moved off. The heterogeneities generate the field perturbation; it is a solution of a similar pair equation. Secondly, we need to define new unknown variables in such way that the pair equation should have the standard form. To get this result we propose to use the boundary value conditions on the heterogeneities. The dual equation is equivalent to regular infinite set of linear equations for the Floquet coefficients. In some case the wave Diffraction Problems on the periodical sets of heterogeneities can be reduced to vector dual summatorial functional equations. © 2012 IEEE

  • Scanning periodic grating: Diffraction Problem and transmission Problem
    2020
    Co-Authors: Pleshchinskii N.
    Abstract:

    The Diffraction Problem and the transmission Problem of quasi-periodic waves on a layered plate with an infinite periodic grating of conducting band are considered. The algorithm of the approximate solution of these Problems is constructed. © 2012 IEEE

  • The uniqueness theorems in the electromagnetic wave theory and quasi-periodical solutions of the periodical Diffraction Problems
    2020
    Co-Authors: Pleshchinskii N.
    Abstract:

    The simple method to prove the uniqueness of the solution of the electromagnetic wave Diffraction Problems is proposed in the case of loss-free media. The set of the Diffraction Problems on the thin conducting screens in the wave-guided structures are considered. The over-determined boundary value Problem method is used. It is shown that the limited absorption principle is correct for the considered Problems. The uniqueness conditions of the solution of the integral equations with difference kernel are obtained as an auxiliary result. These conditions are used to prove the Floquet theorem: the solution of the quasi-periodical wave Diffraction on the periodical set of the heterogeneities can be the quasi-periodical wave (Floquet wave) only. The case of Diffraction Problem on the bi-periodical set of thin conducting screens in the opened space is considered in detail as an example. The boundary value Problem is equivalent to the dual summatorial functional equation for the Floquet coefficients. It is proved that this Problem is equivalent to the regular infinite set of the linear algebraic equations for the coefficients of decomposition of the electromagnetic field by Floquet harmonics. By this set of equations the algorithms are constructed for numerical solving the Diffraction Problem