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Three-dimensional Domains (three-dimensional + domain)
Selected AbstractsNumerical simulation of particle trajectory and atmospheric dispersion of airborne releasesMETEOROLOGICAL APPLICATIONS, Issue 3 2009S. Shoaib Raza Abstract Numerical simulation of particle trajectory and atmospheric dispersion has been performed for an airborne accidental release from a nuclear power plant site. A Long-range Particle transport and Dispersion Model (LPDM) based on a Lagrangian approach is developed and tested in this work. The Lagrangian transport/dispersion model is directly coupled with an atmospheric prediction model, RAMS (Regional Atmospheric Modeling System), to provide necessary meteorological fields in a three-dimensional domain. An advantage of this direct coupling is that the meteorological data generated by RAMS can be used directly for trajectory calculations without storage, thus reducing the CPU time consumed in the data storage and retrieval. This effort was done to be able to use this directly coupled modelling system for real-time predictions in case of an accidental release from a potential site. The simulated Lagrangian trajectories were compared with those obtained using observed hourly weather data obtained from an on-site meteorological tower. The results indicated that this one-way coupling between LPDM-RAMS provided almost identical trajectories when compared with those obtained using LPDM alone driven by hourly observed wind data. The comparison demonstrated the reliability of the RAMS meteorological predictions for the site under consideration. The comparison also indicated that LPDM (run in a stand alone mode), with hourly-observed wind data, could also be used for trajectory calculations over flat terrain. The model was developed on a parallel processing computer (SGI workstation, ORIGIN 2000 computer with eight processors) for use in real-time forecast mode. The computational time was about one-third of the simulation time, while using four processors. The model options need to be explored to reduce the computational time further and test its performance for real-time atmospheric dispersion applications. Copyright © 2009 Royal Meteorological Society [source] Practical CFD Simulations on Programmable Graphics Hardware using SMAC,COMPUTER GRAPHICS FORUM, Issue 4 2005Carlos E. Scheidegger Abstract The explosive growth in integration technology and the parallel nature of rasterization-based graphics APIs (Application Programming Interface) changed the panorama of consumer-level graphics: today, GPUs (Graphics Processing Units) are cheap, fast and ubiquitous. We show how to harness the computational power of GPUs and solve the incompressible Navier-Stokes fluid equations significantly faster (more than one order of magnitude in average) than on CPU solvers of comparable cost. While past approaches typically used Stam's implicit solver, we use a variation of SMAC (Simplified Marker and Cell). SMAC is widely used in engineering applications, where experimental reproducibility is essential. Thus, we show that the GPU is a viable and affordable processor for scientific applications. Our solver works with general rectangular domains (possibly with obstacles), implements a variety of boundary conditions and incorporates energy transport through the traditional Boussinesq approximation. Finally, we discuss the implications of our solver in light of future GPU features, and possible extensions such as three-dimensional domains and free-boundary problems. [source] Computation of a few smallest eigenvalues of elliptic operators using fast elliptic solversINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING, Issue 8 2001Janne Martikainen Abstract The computation of a few smallest eigenvalues of generalized algebraic eigenvalue problems is studied. The considered problems are obtained by discretizing self-adjoint second-order elliptic partial differential eigenvalue problems in two- or three-dimensional domains. The standard Lanczos algorithm with the complete orthogonalization is used to compute some eigenvalues of the inverted eigenvalue problem. Under suitable assumptions, the number of Lanczos iterations is shown to be independent of the problem size. The arising linear problems are solved using some standard fast elliptic solver. Numerical experiments demonstrate that the inverted problem is much easier to solve with the Lanczos algorithm that the original problem. In these experiments, the underlying Poisson and elasticity problems are solved using a standard multigrid method. Copyright © 2001 John Wiley & Sons, Ltd. [source] Multiscale Galerkin method using interpolation wavelets for two-dimensional elliptic problems in general domainsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 2 2004Gang-Won Jang Abstract One major hurdle in developing an efficient wavelet-based numerical method is the difficulty in the treatment of general boundaries bounding two- or three-dimensional domains. The objective of this investigation is to develop an adaptive multiscale wavelet-based numerical method which can handle general boundary conditions along curved boundaries. The multiscale analysis is achieved in a multi-resolution setting by employing hat interpolation wavelets in the frame of a fictitious domain method. No penalty term or the Lagrange multiplier need to be used in the present formulation. The validity of the proposed method and the effectiveness of the multiscale adaptive scheme are demonstrated by numerical examples dealing with the Dirichlet and Neumann boundary-value problems in quadrilateral and quarter circular domains. Copyright © 2003 John Wiley & Sons, Ltd. [source] Orthogonal grids around convex bodies using foliationsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, Issue 5 2003B. Herrera Abstract A new technique for the construction of orthogonal grids around convex bodies is presented. The method, which is analytical or numerical depending on how the body boundary is expressed, is based on the development of geometric foliations that follow a prescribed direction (for instance, the prevailing direction of flow) around convex bodies of arbitrary shape. The construction of these foliations is straightforward and does not require the solution of any system of algebraic or differential equations, nor the use of iterative procedures. The method is applicable both to two- and three-dimensional domains since it is based solely on the concept of local curvature. The lines or surfaces given by the foliations of first and second order, together with the complementary orthogonal lines, respectively, define the orthogonal two- or three-dimensional grids. Copyright © 2002 John Wiley & Sons, Ltd. [source] Flow simulation on moving boundary-fitted grids and application to fluid,structure interaction problemsINTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN FLUIDS, Issue 4 2006Martin Engel Abstract We present a method for the parallel numerical simulation of transient three-dimensional fluid,structure interaction problems. Here, we consider the interaction of incompressible flow in the fluid domain and linear elastic deformation in the solid domain. The coupled problem is tackled by an approach based on the classical alternating Schwarz method with non-overlapping subdomains, the subproblems are solved alternatingly and the coupling conditions are realized via the exchange of boundary conditions. The elasticity problem is solved by a standard linear finite element method. A main issue is that the flow solver has to be able to handle time-dependent domains. To this end, we present a technique to solve the incompressible Navier,Stokes equation in three-dimensional domains with moving boundaries. This numerical method is a generalization of a finite volume discretization using curvilinear coordinates to time-dependent coordinate transformations. It corresponds to a discretization of the arbitrary Lagrangian,Eulerian formulation of the Navier,Stokes equations. Here the grid velocity is treated in such a way that the so-called Geometric Conservation Law is implicitly satisfied. Altogether, our approach results in a scheme which is an extension of the well-known MAC-method to a staggered mesh in moving boundary-fitted coordinates which uses grid-dependent velocity components as the primary variables. To validate our method, we present some numerical results which show that second-order convergence in space is obtained on moving grids. Finally, we give the results of a fully coupled fluid,structure interaction problem. It turns out that already a simple explicit coupling with one iteration of the Schwarz method, i.e. one solution of the fluid problem and one solution of the elasticity problem per time step, yields a convergent, simple, yet efficient overall method for fluid,structure interaction problems. Copyright © 2005 John Wiley & Sons, Ltd. [source] The asymptotic behaviour of weak solutions to the forward problem of electrical impedance tomography on unbounded three-dimensional domainsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 2 2009Michael Lukaschewitsch Abstract The forward problem of electrical impedance tomography on unbounded domains can be studied by introducing appropriate function spaces for this setting. In this paper we derive the point-wise asymptotic behaviour of weak solutions to this problem in the three-dimensional case. Copyright © 2008 John Wiley & Sons, Ltd. [source] Initial boundary value problem for the evolution system of MHD type describing geophysical flow in three-dimensional domainsMATHEMATICAL METHODS IN THE APPLIED SCIENCES, Issue 9 2003Chunshan Zhao Abstract The initial boundary value problem for the evolution system describing geophysical flow in three-dimensional domains was considered. The existence and uniqueness of global strong solution to the evolution system were proved under assumption on smallness of data. Moreover, solvable compatibility conditions of initial data and boundary values which guarantee the existence and uniqueness of global strong solution were discussed. Copyright © 2003 John Wiley & Sons, Ltd. [source] Local minimizers with vortices to the Ginzburg-Landau system in three dimensionsCOMMUNICATIONS ON PURE & APPLIED MATHEMATICS, Issue 1 2004J. Alberto Montero We construct local minimizers to the Ginzburg-Landau energy in certain three-dimensional domains based on the asymptotic connection between the energy and the total length of vortices using the theory of weak Jacobians. Whenever there exists a collection of locally minimal line segments spanning the domain, we can find local minimizers with arbitrarily assigned degrees with respect to each segment. © 2003 Wiley Periodicals, Inc. [source] | |||||||||||||