3D Domain Decomposition Research Articles

多孔質体中を透過する自由水面流れの3次元並列計算

This paper deals with a computational method with multiphase-modeling to predict the 3D free- surface flows through porous media consisting of multiple solid particles like the ground water flows in coarse gravel. In contrast to most of the previous methods, in the present method, the fluid-cells, which are sufficiently finer than the solid particles, are set up in the computational domain and the fluid-solid interactions are accurately calculated by a multiphase-modeling method that needs no empirical parameters such as the drag coefficient Cd. In addition, a parallel computational method is implemented on the basis of the 3D domain decomposition method using MPI. The predicted results are compared with experimental values and further applicability of our method is examined through the numerical experiments for the porous media consisting of randomly-arranged spheroids.

Planar ESPAR Array Design with Nonsymmetrical Pattern by Means of Finite-Element Method, Domain Decomposition, and Spherical Wave Expansion

The application of a 3D domain decomposition finite-element and spherical mode expansion for the design of planar ESPAR (electronically steerable passive array radiator) made with probe-fed circular microstrip patches is presented in this work. A global generalized scattering matrix (GSM) in terms of spherical modes is obtained analytically from the GSM of the isolated patches by using rotation and translation properties of spherical waves. The whole behaviour of the array is characterized including all the mutual coupling effects between its elements. This procedure has been firstly validated by analyzing an array of monopoles on a ground plane, and then it has been applied to synthesize a prescribed radiation pattern optimizing the reactive loads connected to the feeding ports of the array of circular patches by means of a genetic algorithm.

Towards a fully 3D domain-decomposition strategy for water-on-deck phenomena

A numerical approach has been used to analyze the water shipping caused by head sea waves for a FPSO ship at rest. A 3D Domain-Decomposition (DD) strategy is used, where a linear potential-flow seakeeping analysis of the vessel is coupled with a local nonlinear rotational-flow investigation for the prediction of water-on-deck phenomena. The Navier-Stokes solver is applied in the region close to the ship bow. It combines a finite-difference spatial algorithm with a predictor-corrector time scheme. The sea and ship surfaces are tracked with a Level-Set (LS) technique and a hybrid Eulerian-Lagrangian algorithm. The inner solver receives the initial and boundary conditions in terms of velocity, pressure, sea-surface location and ship motions and provides the loads due to the nonlinear wave-ship interaction (including green-water loads) to the seakeeping method. Here the inner solver and its implementation within the DD are described in detail. Preliminary results in terms of water-on-deck occurrence are discussed and compared against 3D water-on-deck experiments.

3D domain decomposition problems, consistent in time and space

AbstractDuring the past years tremendous developments have been achieved in the field of domain decomposition problems as well as in the field of time integration schemes. In the present work actual developments in both fields are merged; the result of this is an extremely stable numerical method in space and in time. (© 2009 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Improved Interface Conditions for 2D Domain Decomposition with Corners: Numerical Applications

This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. After explaining the main results of the theoretical analysis carried out in Chniti et al. (Calcolo 45, 2008), the numerical experiments presented in this article confirm the optimality properties of the new interface conditions.

Improved interface conditions for 2D domain decomposition with corners: a theoretical determination

This article deals with a local improvement of domain decomposition methods for 2-dimensional elliptic problems for which either the geometry or the domain decomposition presents conical singularities. The problem amounts to determining the coefficients of interface boundary conditions so that the domain decomposition algorithm has rapid convergence. Specific problems occur in the presence of conical singularities. Starting from the method used for regular interfaces, we derive a local improvement by matching the singularities, that is, the initial terms of the asymptotic expansion arond the corner, provided by Kondratiev theory. This theoretical approach leads to the explicit computation of coefficients in the interface boundary conditions, which have been tested numerically. This final numerical step is presented in a companion article [4]. This article focuses on the method used to compute these coefficients and provides detailed examples for a model problem.

A parallel 3D Poisson solver for space charge simulation in cylindrical coordinates

This paper presents the development of a parallel three-dimensional Poisson solver in cylindrical coordinate system for the electrostatic potential of a charged particle beam in a circular tube. The Poisson solver uses Fourier expansions in the longitudinal and azimuthal directions, and Spectral Element discretization in the radial direction. A Dirichlet boundary condition is used on the cylinder wall, a natural boundary condition is used on the cylinder axis and a Dirichlet or periodic boundary condition is used in the longitudinal direction. A parallel 2D domain decomposition was implemented in the ( r , θ ) plane. This solver was incorporated into the parallel code PTRACK for beam dynamics simulations. Detailed benchmark results for the parallel solver and a beam dynamics simulation in a high-intensity proton LINAC are presented. When the transverse beam size is small relative to the aperture of the accelerator line, using the Poisson solver in a Cartesian coordinate system and a Cylindrical coordinate system produced similar results. When the transverse beam size is large or beam center located off-axis, the result from Poisson solver in Cartesian coordinate system is not accurate because different boundary condition used. While using the new solver, we can apply circular boundary condition easily and accurately for beam dynamic simulations in accelerator devices.