This paper puts forward an efficient Lattice Boltzmann method for use as a wake simulator suitable for

real-time environments. The method is limited to low speed incompressible flow but is very efficient and

can be used to compute flows “on the fly”. In particular, many-core machines allow for the method to be

used with the need of very expensive parallel clusters. Results are shown here for flows around

cylinders and simple ship shapes

Woodgate, Mark A.

Steijl, Rene

Barakos, George N.

PLoS ONE

English

PubMed

Demonstration of the FPA method to obtain the period for <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163303#pone.0163303.e003" target="_blank">Eq 2</a>: (a) the numerical result of variable y by the PMT method in the interval [0,100]; and (b) variable y in the enlarged interval of [43,45].</p

Pengfei Wang (123133)

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Forward Period Analysis Method of the Periodic Hamiltonian System - Fig 3

The 3 directory in the compressed file is the output of FPA program and the plotting scripts correspondences to figure 1-3.<div> </div

Pengfei Wang (3124368)

Forward period analysis method of the periodic Hamiltonian system  (figure 1-3)

Using the forward period analysis (FPA), we obtain the period of a Morse oscillator and mathematical pendulum system, with the accuracy of 100 significant digits. From these results, the long-term [0, 1060] (time unit) solutions, ranging from the Planck time to the age of the universe, are computed reliably and quickly with a parallel multiple-precision Taylor series (PMT) scheme. The application of FPA to periodic systems can greatly reduce the computation time of long-term reliable simulations. This scheme provides an efficient way to generate reference solutions, against which long-term simulations using other schemes can be tested

Pengfei Wang

Directory of Open Access Journals

Forward Period Analysis Method of the Periodic Hamiltonian System.

The direct simulation of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163303#pone.0163303.e014" target="_blank">Eq 5</a> by the 20-order PMT method, with a step-size of h = 0.01: (a) Hamiltonian H, (b) variable p versus time (the first 20 time units).</p

Forward Period Analysis Method of the Periodic Hamiltonian System - Fig 2

Illustrations of the direct simulation of <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0163303#pone.0163303.e003" target="_blank">Eq 2</a>: (a) variable x by PMT; (b) error of x computed by the SE2 method; (c) structure of the x-p plane by PMT; (d) the Hamiltonian H by PMT to T = 107; (e) error of the Hamiltonian H by the SE2 method. Panels (a–c) have step-size h = 0.01; (d–e) have step-size h = 0.1.</p

Forward Period Analysis Method of the Periodic Hamiltonian System - Fig 1

Wang Pengfei

Public Library of Science (PLOS)

Forward Period Analysis Method of the Periodic Hamiltonian System

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