Transmission and reflection of long waves over steep bathymetry variat ons using large floating strips of Shallow draft

The present study focuses on the determination of reflection and transmission characteristics for the coupled hydroelastic system involving a strip of large extent and shallow draft, floating over steep bathymetric variations and interacting with long waves. A parametric analysis with respect to the floating strip stiffness and the magnitude of the bathymetry variation for specific seabed profiles is conducted. This parametric study is expected to indicate optimum design characteristics, in terms of the strip flexural rigidity, for maximizing long wave reflection or transmission, depending on the specific application

Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field

Higher-order fem for nonlinear hydroelastic analysis of a floating elastic strip in shallow-water conditions

The hydroelastic response of a thin, nonlinear, elastic strip floating in shalow-water environment is studied by means of a special higher order finite element scheme. Considering non-negligible stress variation in lateral direction, the nonlinear beam model, developed by Gao, is used for the simulation of large flexural displacement. Full hydroelastic coupling between the floating strip and incident waves is assumed. The derived set of equations is intended to serve as a simplified model for tsunami impact on Very Large Floating Structures (VLFS) or ice floes. The proposed finite element method incorporates Hermite polynomials of fifth degree for the approximation of the beam deflection/upper surface elevation in the hydroelastic coupling region and 5-node Lagrange finite elements for the simulation of the velocity potential in the water region. The resulting second order ordinary differential equation system is converted into a first order one and integrated with respect to time with the Crank-Nicolson method. Two distinct cases of long wave forcing, namely an elevation pulse and an N-wave pulse, are considered. Comparisons against the respective results of the standard, linear Euler-Bernoulli floating beam model are performed and the effect of large displacement in the beam response is studied

Thermo-mechanical response FEM simulation of ceramic refractories undergoing severe temperature variations

T. K Papathanasiou and F. Dal Corso gratefully acknowledge support from the European Union FP7 project “Mechanics of refractory materials at high–temperature for advanced industrial technologies” under contract number PIAPP–GA–2013–609758. A. Piccolroaz would like to acknowledge financial support from the European Union‟s Seventh Framework Programme FP7/2007-2013/ under REA grant agreement number PITN-GA-2013-606878-CERMAT2

Transmission and reflection of long waves over steep bathymetry variat ons using large floating strips of Shallow draft

The present study focuses on the determination of reflection and transmission characteristics for the coupled hydroelastic system involving a strip of large extent and shallow draft, floating over steep bathymetric variations and interacting with long waves. A parametric analysis with respect to the floating strip stiffness and the magnitude of the bathymetry variation for specific seabed profiles is conducted. This parametric study is expected to indicate optimum design characteristics, in terms of the strip flexural rigidity, for maximizing long wave reflection or transmission, depending on the specific application

Error estimates for a FitzHugh–Nagumo parameter-dependent reaction-diffusion system

Space-time approximations of the FitzHugh–Nagumo system of coupled semi-linear parabolic PDEs are examined. The schemes under consideration are discontinuous in time but conforming in space and of arbitrary order. Stability estimates are presented in the natural energy norms and at arbitrary times, under minimal regularity assumptions. Space-time error estimates of arbitrary order are derived, provided that the natural parabolic regularity is present. Various physical parameters appearing in the model are tracked and numerical examples are presented

Propagation of acoustic-gravity waves in inhomogeneous ocean environment based on modal expansions and HP-FEM

A coupled mode model is presented for the propagation of acoustic-gravity waves in layered ocean waveguides. The analysis extends previous work for acoustic waves in inhomogeneous environment. The coupled mode system is derived by means of a variational principle in conjunction with local mode series expansion, obtained by utilizing eigenfunction systems defined in the vertical section. These are obtained through the solution of vertical eigenvalue problems formulated along the waveguide. A crucial factor is the inclusion of additional modes accounting for the effects of spatialy varying boundaries and interfaces. This enhancement provides an implicit summation for the slowly convergent part of the localmode series, rendering the series rapidly convergent, increasing substantialy the efficiency of the method. Particular aspects of the method include high order Lagrange Finite Element Methods for the solution of local vertical eigenvalue problems in the case of multilayered waveguides, and Gauss-type quadrature for the computation of the coupled-mode system coefficients. The above aspects make the present method quite efficient for long range propagation in extended waveguides, such as the ones found in geophysical applications, e.g. ocean basins, as only few modes are needed for the accurate representation of the wave field

Higher-order fem for nonlinear hydroelastic analysis of a floating elastic strip in shallow-water conditions

The hydroelastic response of a thin, nonlinear, elastic strip floating in shalow-water environment is studied by means of a special higher order finite element scheme. Considering non-negligible stress variation in lateral direction, the nonlinear beam model, developed by Gao, is used for the simulation of large flexural displacement. Full hydroelastic coupling between the floating strip and incident waves is assumed. The derived set of equations is intended to serve as a simplified model for tsunami impact on Very Large Floating Structures (VLFS) or ice floes. The proposed finite element method incorporates Hermite polynomials of fifth degree for the approximation of the beam deflection/upper surface elevation in the hydroelastic coupling region and 5-node Lagrange finite elements for the simulation of the velocity potential in the water region. The resulting second order ordinary differential equation system is converted into a first order one and integrated with respect to time with the Crank-Nicolson method. Two distinct cases of long wave forcing, namely an elevation pulse and an N-wave pulse, are considered. Comparisons against the respective results of the standard, linear Euler-Bernoulli floating beam model are performed and the effect of large displacement in the beam response is studied