Download User Manual SmoothViz - Visualization and Computer Graphics

Introduction
Hamiltonian Particle-Mesh method (HPM) method was proposed by J. Frank, G. Gottwald
and S. Reich [1, 2, 3]. The authors modified ideas of Smoothed Particle Hydrodynamics (SPH)
and Particle-in-Cell algorithms. The new Lagrangian-Eulerian method was successfully applied for numerical solution of Shallow Water Equations (SWE), which are extensively used
to simulate geophysical processes. HPM is a hybrid numerical method. It has a natural adaptivity property like most particle methods. At the same time it incorporates the procedure of
artificial smoothing of the depth field over a regular grid into the classical Lagrangian formalism. Usually the inverse Helmholtz operator is applied. This smoothing reduces the numerical
noise and can be viewed as an efficient implementation of SPH for globally supported basis
functions.
Many recent studies have focused on robustness, accuracy and conservation properties of
the HPM method. It was shown that HPM equations inherit the Hamiltonian structure of
SWE, advect the potential vorticity properly and have better long-time stability properties than
SPH. This was also tested in a number of numerical experiments [4]. However, little research
has been done in the field of optimization of the method and analytical investigation of its
convergence.
There are three characteristic scales for the system of N interacting particles in d-dimensional
space, whose evolution is governed by HPM equations. They are: The artificial smoothing
length µ, the average particle distance lpart and the mesh size λ . The interrelation of the scales
is a subject of recent study [5].
HPMviz is a tool which serves to perform simulations using HPM method, investigate the
behavior of the solution with respect to the key parameters (µ, lpart , λ , type of the kernel
functions, etc.), and visualize the results. It has been (and is still being) developed at Visualization and Computer Graphics Laboratory (VCGL), Jacobs University, Bremen, Germany
(http://vcgl.jacobs-university.de).
1
General information
The code is written in C++. Fourier transformations are performed using FFTW library. We
used OpenGL for 3D visualization and GLSL for the Phong shading. The GUI was developed
in Qt 4.7.
1.1
License
This program is free software; you can redistribute it under the terms of the GNU General
Public License as published by the Free Software Foundation; either version 3 of the License.
This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A
PARTICULAR PURPOSE. See the GNU General Public License for more details.
3