Near conserving energy numerical schemes for two-dimensional coupled seismic wave equations

Two-dimensional coupled seismic waves, satisfying the equations of linear isotropic elasticity, on a rectangular domain with initial conditions and periodic boundary conditions, are considered. A quantity conserved by the solution of the continuous problem is used to check the numerical solution of the problem. Second order spatial derivatives, in the x direction, in the y direction and mixed derivative, are approximated by finite differences on a uniform grid. The ordinary second order in time system obtained is transformed into a first order in time system in the displacement and velocity vectors. For the time integration of this system, second order and fourth order exponential splitting methods, which are geometric integrators, are proposed. These explicit splitting methods are not unconditionally stable and the stability condition for time step and space step ratio is deduced. Numerical experiments displaying the good behavior in the long time integration and the efficiency of the numerical solution are provided.MTM2015-66837-P del Ministerio de Economía y Competitivida

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Generalized averaged Gaussian quadrature and applications

A simple numerical method for constructing the optimal generalized averaged Gaussian quadrature formulas will be presented. These formulas exist in many cases in which real positive GaussKronrod formulas do not exist, and can be used as an adequate alternative in order to estimate the error of a Gaussian rule. We also investigate the conditions under which the optimal averaged Gaussian quadrature formulas and their truncated variants are internal

MS FT-2-2 7 Orthogonal polynomials and quadrature: Theory, computation, and applications

Quadrature rules find many applications in science and engineering. Their analysis is a classical area of applied mathematics and continues to attract considerable attention. This seminar brings together speakers with expertise in a large variety of quadrature rules. It is the aim of the seminar to provide an overview of recent developments in the analysis of quadrature rules. The computation of error estimates and novel applications also are described

Survivability of Wave Energy Converter and Mooring Coupled System using CFD

Full version unavailable due to 3rd party copyright restrictions.This thesis discusses the development of a Numerical Wave Tank (NWT) capable of describing the coupled behaviour of Wave Energy Converters (WECs) and their moorings under extreme wave loading. The NWT utilises the open-source Computational Fluid Dynamics (CFD) software OpenFOAM(R) to solve the fully nonlinear, incompressible, Reynolds-Averaged Navier-Stokes (RANS) equations for air and water using the Finite Volume Method (FVM) and a Volume of Fluid (VOF) treatment of the interface. A method for numerically generating extreme waves is devised, based on the dispersively-focused NewWave theory and using the additional toolbox waves2Foam. A parametric study of the required mesh resolution shows that steeper waves require finer grids for mesh independence. Surface elevation results for wave-only cases closely match those from experiments, although an improved definition of the flow properties is required to generate very steep focused waves. Predictions of extreme wave run-up and pressure on the front of a fixed truncated cylinder compare well with physical measurements; the numerical solution successfully predicts the secondary loading cycle associated with the nonlinear ringing effect and shows a nonlinear relationship between incident crest height and horizontal load. With near perfect agreement during an extreme wave event, the reproduction of the six degree of freedom (6DOF) motion and load in the linearly-elastic mooring of a hemispherical-bottomed buoy significantly improves on similar studies from the literature. Uniquely, this study compares simulations of two existing WEC designs with scale-model tank tests. For the Wavestar machine, a point-absorber constrained to pitch motion only, results show good agreement with physical measurements of pressure, force and float motion in regular waves, although the solution in the wake region requires improvement. Adding bespoke functionality, a point-absorber designed by Seabased AB, consisting of a moored float and Power Take-Off (PTO) with limited stroke length, translator and endstop, is modelled in large regular waves. This represents a level of complexity not previously attempted in CFD and the 6DOF float motion and load in the mooring compare well with experiments. In conclusion, the computational tool developed here is capable of reliably predicting the behaviour of WEC systems during extreme wave events and, with some additional parameterisation, could be used to assess the survivability of WEC systems at full-scale before going to the expense of deployment at sea.Engineering and Physical Sciences Research Council (EPSRC) via SuperGen UK Centre for Marine Energy Research (UKCMER