Numerical solution of the two-dimensional Gross-Pitaevskii equation for trapped interacting atoms

We present a numerical scheme for solving the time-independent nonlinear Gross-Pitaevskii equation in two dimensions describing the Bose-Einstein condensate of trapped interacting neutral atoms at zero temperature. The trap potential is taken to be of the harmonic-oscillator type and the interaction both attractive and repulsive. The Gross-Pitaevskii equation is numerically integrated consistent with the correct boundary conditions at the origin and in the asymptotic region. Rapid convergence is obtained in all cases studied. In the attractive case there is a limit Co the maximum number of atoms in the condensate. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Numerical simulation of viscous three-dimensional flow over aerospace vehicles using Euler/boundary-layer zonal approach

This paper presents a viscous three-dimensional simulations coupling Euler and boundary layer codes for calculating flows over arbitrary surfaces. The governing equations are written in a general non orthogonal coordinate system. The Levy-Lees transformation generalized to three-dimensional flows is utilized. The inviscid properties are obtained from the Euler equations using the Beam and Warming implicit approximate factorization scheme. The resulting equations are discretized and approximated by a two-point fmitedifference numerical scheme. The code developed is validated and applied to the simulation of the flowfield over aerospace vehicle configurations. The results present good correlation with the available data.

High-order upwinding and the hydraulic jump

This work is concerned with the computation of incompressible axisymmetric and fall three-dimensional free-surface flows. In particular, the circular-hydraulic jump is simulated and compared with approximate analytic solutions. However, the principal thrust of this paper is to provide a real problem as a test bed for comparing the many existing convective approximations. Their performance is compared; SMART, HLPA and VONOS emerge as acceptable upwinding methods for this problem. Copyright (C) 2002 John Wiley Sons, Ltd.

Escape and transport for an open bouncer: Stretched exponential decays

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

The element-free Galerkin method applied to the study of fully developed magnetohydrodynamic duct flows

In this paper, the meshless method is introduced to magnetohydrodynamics. A numerical scheme based on the element-free Galerkin method is used to solve the laminar steady-state two-dimensional fully developed magnetohydrodynamic flow in a rectangular duct. Accurate and convergent solutions are achieved for low to moderately high Hartmann numbers.

Three-dimensional finite element analysis of MHD duct flow by the penalty function formulation

A numerical scheme based on the Finite Element Method (FEM) is presented to calculate the full solution of a three-dimensional steady magnetohydrodynamic (MHD) flow with moderately high Hartmann numbers and interaction parameters. An incompressible, viscous and electrically conducting liquid-metal is considered. Assuming a low magnetic Reynolds number, the solution method solves the coupled Navier-Stokes and Maxwell's equations through the use of a penalty function method. Results are presented for Hartmann numbers in the range 10(2)-10(3).

A Transmission Problem for Euler-Bernoulli beam with Kelvin-Voigt Damping

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Stability analysis of Crank-Nicolson and Euler schemes for time-dependent diffusion equations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A bounded upwinding scheme for computing convection-dominated transport problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A continuously differentiable upwinding scheme for the simulation of fluid flow problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A fully adaptive multiresolution scheme for shock computations

The scheme is based on Ami Harten's ideas (Harten, 1994), the main tools coming from wavelet theory, in the framework of multiresolution analysis for cell averages. But instead of evolving cell averages on the finest uniform level, we propose to evolve just the cell averages on the grid determined by the significant wavelet coefficients. Typically, there are few cells in each time step, big cells on smooth regions, and smaller ones close to irregularities of the solution. For the numerical flux, we use a simple uniform central finite difference scheme, adapted to the size of each cell. If any of the required neighboring cell averages is not present, it is interpolated from coarser scales. But we switch to ENO scheme in the finest part of the grids. To show the feasibility and efficiency of the method, it is applied to a system arising in polymer-flooding of an oil reservoir. In terms of CPU time and memory requirements, it outperforms Harten's multiresolution algorithm.The proposed method applies to systems of conservation laws in 1Dpartial derivative(t)u(x, t) + partial derivative(x)f(u(x, t)) = 0, u(x, t) is an element of R-m. (1)In the spirit of finite volume methods, we shall consider the explicit schemeupsilon(mu)(n+1) = upsilon(mu)(n) - Deltat/hmu ((f) over bar (mu) - (f) over bar (mu)-) = [Dupsilon(n)](mu), (2)where mu is a point of an irregular grid Gamma, mu(-) is the left neighbor of A in Gamma, upsilon(mu)(n) approximate to 1/mu-mu(-) integral(mu-)(mu) u(x, t(n))dx are approximated cell averages of the solution, (f) over bar (mu) = (f) over bar (mu)(upsilon(n)) are the numerical fluxes, and D is the numerical evolution operator of the scheme.According to the definition of (f) over bar (mu), several schemes of this type have been proposed and successfully applied (LeVeque, 1990). Godunov, Lax-Wendroff, and ENO are some of the popular names. Godunov scheme resolves well the shocks, but accuracy (of first order) is poor in smooth regions. Lax-Wendroff is of second order, but produces dangerous oscillations close to shocks. ENO schemes are good alternatives, with high order and without serious oscillations. But the price is high computational cost.Ami Harten proposed in (Harten, 1994) a simple strategy to save expensive ENO flux calculations. The basic tools come from multiresolution analysis for cell averages on uniform grids, and the principle is that wavelet coefficients can be used for the characterization of local smoothness.. Typically, only few wavelet coefficients are significant. At the finest level, they indicate discontinuity points, where ENO numerical fluxes are computed exactly. Elsewhere, cheaper fluxes can be safely used, or just interpolated from coarser scales. Different applications of this principle have been explored by several authors, see for example (G-Muller and Muller, 1998).Our scheme also uses Ami Harten's ideas. But instead of evolving the cell averages on the finest uniform level, we propose to evolve the cell averages on sparse grids associated with the significant wavelet coefficients. This means that the total number of cells is small, with big cells in smooth regions and smaller ones close to irregularities. This task requires improved new tools, which are described next.

A combination of implicit and adaptative upwind tools for the numerical solution of incompressible free surface flows

This paper is concerned with the numerical solutions of time dependent two-dimensional incompressible flows. By using the primitive variables of velocity and pressure, the Navier-Stokes and mass conservation equations are solved by a semi-implicit finite difference projection method. A new bounded higher order upwind convection scheme is employed to deal with the non-linear (advective) terms. The procedure is an adaptation of the GENSMAC (J. Comput. Phys. 1994; 110: 171-186) methodology for calculating confined and free surface fluid flows at both low and high Reynolds numbers. The calculations were performed by using the 2D version of the Freeflow simulation system (J. Comp. Visual. Science 2000; 2:199-210). In order to demonstrate the capabilities of the numerical method, various test cases are presented. These are the fully developed flow in a channel, the flow over a backward facing step, the die-swell problem, the broken dam flow, and an impinging jet onto a flat plate. The numerical results compare favourably with the experimental data and the analytical solutions. Copyright (c) 2006 John Wiley & Sons, Ltd.

Evaluation of a bounded high order upwind scheme for 3D incompressible free surface flow computations

fit the context of normalized variable formulation (NVF) of Leonard and total variation diminishing (TVD) constraints of Harten. this paper presents an extension of it previous work by the authors for solving unsteady incompressible flow problems. The main contributions of the paper are threefold. First, it presents the results of the development and implementation of a bounded high order upwind adaptative QUICKEST scheme in the 3D robust code (Freeflow), for the numerical solution of the full incompressible Navier-Stokes equations. Second, it reports numerical simulation results for 1D hock tube problem, 2D impinging jet and 2D/3D broken clam flows. Furthermore, these results are compared with existing analytical and experimental data. and third, it presents the application of the numerical method for solving 3D free surface flow problems. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved,

Assessment of a high-order finite difference upwind scheme for the simulation of convection-diffusion problems

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Simulation results and applications of an advection bounded scheme to practical flows

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)