Cambridge University Press. Paperback. Book Condition: New. Paperback. 480 pages. Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The exposition maintains a balance between theoretical, algorithmic and applied aspects. This new edition has been extensively updated, and includes new chapters on emerging subject areas: geometric numerical integration, spectral methods and conjugate gradients. Other topics covered include multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; and a variety of algorithms to solve large, sparse algebraic systems. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Paperback.

A First Course in the Numerical Analysis of Differential Equations: Stiff equations

Forcing by steep regular water waves on a vertical circular cylinder at finite depth was investigated numerically by solving the two-phase incompressible Navier–Stokes equations. Consistently with potential flow theory, boundary layer effects were neglected at the sea bed and at the cylinder surface, but the strong nonlinear motion of the free surface was included. The numerical model was verified and validated by grid convergence and by comparison to relevant experimental measurements. First-order convergence towards an analytical solution was demonstrated and an excellent agreement with the experimental data was found. Time-domain computations of the normalized inline force history on the cylinder were analysed as a function of dimensionless wave height, water depth and wavelength. Here the dependence on depth was weak, while an increase in wavelength or wave height both lead to the formation of secondary load cycles. Special attention was paid to this secondary load cycle and the flow features that cause it. By visual observation and a simplified analytical model it was shown that the secondary load cycle was caused by the strong nonlinear motion of the free surface which drives a return flow at the back of the cylinder following the passage of the wave crest. The numerical computations were further analysed in the frequency domain. For a representative example, the secondary load cycle was found to be associated with frequencies above the fifth- and sixth-harmonic force component. For the third-harmonic force, a good agreement with the perturbation theories of Faltinsen, Newman & Vinje (J. Fluid Mech., vol. 289, 1995, pp. 179–198) and Malenica & Molin (J. Fluid Mech., vol. 302, 1995, pp. 203–229) was found. It was shown that the third-harmonic forces were estimated well by a Morison force formulation in deep water but start to deviate at decreasing depth.

Forcing of a bottom-mounted circular cylinder by steep regular water waves at finite depth

An efficient domain decomposition strategy for wave loads on surface piercing circular cylinders

DualSPHysics is a weakly compressible smoothed particle hydrodynamics (SPH) Navier-Stokes solver initially conceived to deal with coastal engineering problems, especially those related to wave impact with coastal structures. Since the first release back in 2011, DualSPHysics has shown to be robust and accurate for simulating extreme wave events along with a continuous improvement in efficiency thanks to the exploitation of hardware such as graphics processing units (GPUs) for scientific computing or the coupling with wave propagating models such as SWASH and OceanWave3D. Numerous additional functionalities have also been included in the DualSPHysics package over the last few years which allow the simulation of fluid-driven objects. The use of the discrete element method (DEM) has allowed the solver to simulate the interaction among different bodies (sliding rocks, for example), which provides a unique tool to analyse debris flows. In addition, the recent coupling with other solvers like Project Chrono or MoorDyn has been a milestone in the development of the solver. Project Chrono allows the simulation of articulated structures with joints, hinges, sliders and springs and MoorDyn allows simulating moored structures. Both functionalities make DualSPHysics one of the meshless model world leaders in the simulation of offshore energy harvesting devices. Lately, the present state of maturity of the solver goes beyond single phase simulations, allowing multi-phase simulations with gas-liquid and a combination of Newtonian and non-Newtonian models expanding further the capabilities and range of applications for the DualSPHysics solver. These advances and functionalities make DualSPHysics a state-of-the-art meshless solver with emphasis on free-surface flow modelling.

State-of-the-art SPH solver DualSPHysics: from fluid dynamics to multiphysics problems.

A harmonic polynomial cell (HPC) method for 3D Laplace equation with application in marine hydrodynamics

An efficient flexible-order model for 3D nonlinear water waves

https://backend.orbit.dtu.dk/ws/files/127446530/1_s2.0_S1876610216308657_main.pdf

DeRisk - Accurate prediction of ULS wave loads. Outlook and first results

Fast hydrodynamics on heterogenous many-core hardware

We present recent and preliminary work directed towards the development of a simplified, physics-based model for improved simulation of ship-ship interaction that can be used for both analysis and real-time computing (i.e. with real-time constraints due to visualization). The goal is to implement the model into a large maritime simulator for training of naval officers, in particular tug boat helmsmen. Tug boat simulators are used for training of communication and situation awareness during manoeuvre involved with towing of large vessels. A main objective of the work is to improve and enable more accurate (realistic) and much faster ship-wave and shipship simulations than are currently possible. The coupling of simulation with visualization should improve the visual experience such that it can be perceived as more realistic in training. Today the state-of-art in real-time ship-ship interaction is for efficiency reasons and time-constraints in visualization based on model experiments in towing tanks and precomputed force tables. We anticipate that the fast, and highly parallel, algorithm described by Engsig-Karup et al. [2011] for execution on affordable modern high-throughput Graphics Processing Units (GPUs) can provide the basis for efficient simulations in combination with an accurate free-surface model for ShipShip simulation. Another area of application is the determination of wave disturbances from a ship in a coastal environment, channels and harbours. The model proposed in the following can in a simple and efficient way calculate the wave field from a ship sailing in a finite depth sea, even with variations in the height of sea bed. The generated wave field can be applied as an input to other models that simulate the marine environment on a larger scale.

/pdf/towards-real-time-simulation-of-ship-ship-interaction-er6ehqg3tc.pdf

Towards Real Time Simulation of Ship-Ship Interaction

For robust nonlinear wave simulation in a moving reference frame, we recast the free surface problem in Hamilton-Jacobi form and propose a Weighted Essentially Non-Oscillatory (WENO) scheme to automatically handle the upwinding of the convective term. A new automatic procedure for deriving the linear WENO weights based on a Taylor series expansion is introduced. A simplified smoothness indicator is proposed and is shown to perform well. The scheme is combined with high-order explicit Runge-Kutta time integration and a dissipative Lax-Friedrichs-type flux to solve for nonlinear wave propagation in a moving frame of reference. The WENO scheme is robust and less dissipative than the equivalent order upwind-biased finite difference scheme for all ratios of frame of reference to wave propagation speed tested. This provides the basis for solving general nonlinear wave-structure interaction problems at forward speed.

/pdf/a-robust-weno-scheme-for-nonlinear-waves-in-a-moving-57m3ksz6fx.pdf

A robust WENO scheme for nonlinear waves in a moving reference frame

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