Large Scale Numerical Simulations For Multi-Phase Fluid Dynamics With Moving Interfaces

This short communication presents our recent studies to implement numerical simulations for multi-phase flows on top-ranked supercomputer systems with distributed memory architecture. The numerical model is designed so as to make full use of the capacity of the hardware. Satisfactory scalability in terms of both the parallel speed-up rate and the size of the problem has been obtained on two high rank systems with massively parallel processors, the Earth Simulator (Earth simulator research center, Yokohama Kanagawa, Japan) and the TSUBAME (Tokyo Institute of Technology, Tokyo, Japan) supercomputers.

Algorithms for colour image processing based on neurological models

373 p. : il., gráf., fot., tablas

Numerical Simulation of R-M Instability

In order to capture shock waves and contact discontinuities in the field and easy to program with parallel computation a new algorithm is developed to solve the N-S equations for simulation of R-M instability problems. The method with group velocity control is used to suppress numerical oscillations, and an adaptive non-uniform mesh is used to get fine resolution. Numerical results for cylindrical shock-cylindrical interface interaction with a shock Mach number Ms=1.2 and Atwood number A=0.818, 0.961, 0.980 (the interior density of the interface/outer density p(1)/p(2) = 10, 50, 100, respectively), and for the planar shock-spherical interface interaction with Ms=1.2 and p(1)/p(2) = 14.28are presented. The effect of Atwood number and multi-mode initial perturbation on the R-M instability are studied. Multi-collisions of the reflected shock with the interface is a main reason of nonlinear development of the interface instability and formation of the spike-bubble structures In simulation with double mode perturbation vortex merging and second instability are found. After second instability the small vortex structures near the interface produced. It is important factor for turbulent mixing.

A block SPP algorithm for multidimensional tridiagonal equations with optimal message vector length

A parallel strategy for solving multidimensional tridiagonal equations is investigated in this paper. We present in detail an improved version of single parallel partition (SPP) algorithm in conjunction with message vectorization, which aggregates several communication messages into one to reduce the communication cost. We show the resulting block SPP can achieve good speedup for a wide range of message vector length (MVL), especially when the number of grid points in the divided direction is large. Instead of only using the largest possible MVL, we adopt numerical tests and modeling analysis to determine an optimal MVL so that significant improvement in speedup can be obtained.

Asymptotic scaling in the two-dimensional O(3) Nonlinear sigma model: a Monte Carlo study on parallel computers

We investigate the 2d O(3) model with the standard action by Monte Carlo simulation at couplings β up to 2.05. We measure the energy density, mass gap and susceptibility of the model, and gather high statistics on lattices of size L ≤ 1024 using the Floating Point Systems T-series vector hypercube and the Thinking Machines Corp.'s Connection Machine 2. Asymptotic scaling does not appear to set in for this action, even at β = 2.10, where the correlation length is 420. We observe a 20% difference between our estimate m/Λ^─_(Ms) = 3.52(6) at this β and the recent exact analytical result . We use the overrelaxation algorithm interleaved with Metropolis updates and show that decorrelation time scales with the correlation length and the number of overrelaxation steps per sweep. We determine its effective dynamical critical exponent to be z' = 1.079(10); thus critical slowing down is reduced significantly for this local algorithm that is vectorizable and parallelizable.

We also use the cluster Monte Carlo algorithms, which are non-local Monte Carlo update schemes which can greatly increase the efficiency of computer simulations of spin models. The major computational task in these algorithms is connected component labeling, to identify clusters of connected sites on a lattice. We have devised some new SIMD component labeling algorithms, and implemented them on the Connection Machine. We investigate their performance when applied to the cluster update of the two dimensional Ising spin model.

Finally we use a Monte Carlo Renormalization Group method to directly measure the couplings of block Hamiltonians at different blocking levels. For the usual averaging block transformation we confirm the renormalized trajectory (RT) observed by Okawa. For another improved probabilistic block transformation we find the RT, showing that it is much closer to the Standard Action. We then use this block transformation to obtain the discrete β-function of the model which we compare to the perturbative result. We do not see convergence, except when using a rescaled coupling β_E to effectively resum the series. For the latter case we see agreement for m/ Λ^─_(Ms) at , β = 2.14, 2.26, 2.38 and 2.50. To three loops m/Λ^─_(Ms) = 3.047(35) at β = 2.50, which is very close to the exact value m/ Λ^─_(Ms) = 2.943. Our last point at β = 2.62 disagrees with this estimate however.

MODIFIED DIRECT TWOS-COMPLEMENT PARALLEL ARRAY MULTIPLICATION ALGORITHM FOR COMPLEX MATRIX OPERATION

A direct twos-complement parallel array multiplication algorithm is introduced and modified for digital optical numerical computation. The modified version overcomes the problems encountered in the conventional optical twos-complement algorithm. In the array, all the summands are generated in parallel, and the relevant summands having the same weights are added simultaneously without carries, resulting in the product expressed in a mixed twos-complement system. In a two-stage array, complex multiplication is possible with using four real subarrays. Furthermore, with a three-stage array architecture, complex matrix operation is straightforwardly accomplished. In the experiment, parallel two-stage array complex multiplication with liquid-crystal panels is demonstrated.

Parallel optical negabinary signed-digit computing: algorithm and optical implementation

Negabinary is a component of the positional number system. A complete set of negabinary arithmetic operations are presented, including the basic addition/subtraction logic, the two-step carry-free addition/subtraction algorithm based on negabinary signed-digit (NSD) representation, parallel multiplication, and the fast conversion from NSD to the normal negabinary in the carry-look-ahead mode. All the arithmetic operations can be performed with binary logic. By programming the binary reference bits, addition and subtraction can be realized in parallel with the same binary logic functions. This offers a technique to perform space-variant arithmetic-logic functions with space-invariant instructions. Multiplication can be performed in the tree structure and it is simpler than the modified signed-digit (MSD) counterpart. The parallelism of the algorithms is very suitable for optical implementation. Correspondingly, a general-purpose optical logic system using an electron trapping device is suggested. Various complex logic functions can be performed by programming the illumination of the data arrays without additional temporal latency of the intermediate results. The system can be compact. These properties make the proposed negabinary arithmetic-logic system a strong candidate for future applications in digital optical computing with the development of smart pixel arrays. (C) 1999 Society of Photo-Optical Instrumentation Engineers. [S0091-3286(99)00803-X].

Fast numerical methods for mixed, singular Helmholtz boundary value problems and Laplace eigenvalue problems - with applications to antenna design, sloshing, electromagnetic scattering and spectral geometry

This thesis presents a novel class of algorithms for the solution of scattering and eigenvalue problems on general two-dimensional domains under a variety of boundary conditions, including non-smooth domains and certain "Zaremba" boundary conditions - for which Dirichlet and Neumann conditions are specified on various portions of the domain boundary. The theoretical basis of the methods for the Zaremba problems on smooth domains concern detailed information, which is put forth for the first time in this thesis, about the singularity structure of solutions of the Laplace operator under boundary conditions of Zaremba type. The new methods, which are based on use of Green functions and integral equations, incorporate a number of algorithmic innovations, including a fast and robust eigenvalue-search algorithm, use of the Fourier Continuation method for regularization of all smooth-domain Zaremba singularities, and newly derived quadrature rules which give rise to high-order convergence even around singular points for the Zaremba problem. The resulting algorithms enjoy high-order convergence, and they can tackle a variety of elliptic problems under general boundary conditions, including, for example, eigenvalue problems, scattering problems, and, in particular, eigenfunction expansion for time-domain problems in non-separable physical domains with mixed boundary conditions.

Um metodo numerico com paralelismo no tempo para aproximar solucoes de EDPs

Este trabalho de pesquisa tem por objetivo apresentar e investigar a viabilidade de um método numérico que contempla o paralelismo no tempo. Este método numérico está associado a problemas de condição inicial e de contorno para equações diferenciais parciais (evolutivas). Diferentemente do método proposto neste trabalho, a maioria dos métodos numéricos associados a equações diferencias parciais evolutivas e tradicionalmente encontrados, contemplam apenas o paralelismo no espaço. Daí, a motivação em realizar o presente trabalho de pesquisa, buscando não somente um método com paralelismo no tempo mas, sobretudo, um método viável do ponto de vista computacional. Para isso, a implementação do esquema numérico proposto está por conta de um algoritmo paralelo escrito na linguagem C e que utiliza a biblioteca MPI. A análise dos resultados obtidos com os testes de desempenho revelam um método numérico escalável e que exige pouco nível de comunicação entre processadores.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (2nd report, direct numerical simulation using townsend's eddy forcing)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method using 'simple model eddies' (Townsend 1976) for DNS of stationary homogeneous isotropic turbulence is proposed. A force field is obtained in real space by sprinkling many space-filling 'simple model eddies' whose centers are randomly but uniformly distributed in space and whose axes of rotation are random. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects are investigated. The results show that stationary homogeneous isotropic turbulence is generated in real space using the present method. By using different model eddies with different sizes and rotation speeds, we could change the turbulence properties such as the integral and micro scales, the turbulent Reynolds number and the isotropy of turbulence. Turbulence intensities near the wall showed good agreements with the previous measurement and the linear analysis based on a rapid distortion theory (RDT). The splat effect (i.e., turbulence intensities of the components parallel to the boundary are amplified) occurs near the boundary and the viscous effect prohibits the splat effect at the quasi steady state at low Reynolds number.

Reynolds number influence on turbulent blocking effects of a rigid plane boundary (3rd report, direct numerical simulation on wall blocking effects for anisotropic turbulence)

The Reynolds number influence on turbulent blocking effects by a rigid plane boundary is studied using direct numerical simulation (DNS). A new forcing method proposed in the second report using Townsend's "simple model eddies" for DNS was extended to generate axisymmetric anisotropic turbulence. A force field is obtained in real space by sprinkling many space-filling "simple model eddies" whose centers are randomly but uniformly distributed in space. The axes of rotation are controlled in this study to generate axisymmetric anisotropic turbulence. The method is applied to a shear-free turbulent boundary layer over a rigid plane boundary and the blocking effects for anisotropic turbulence are investigated. The results show that stationary axisymmetric anisotropic turbulence is generated using the present method. Turbulence intensities near the wall showed good agreements with the rapid distortion theory (RDT) for small t (t ≪ TL), where TL. is the eddy turnover time. The splat effect (i. e. turbulence intensities of the components parallel to the surface are amplified) occurs near the boundary and the viscous effect attenuates the splat effect at the quasi steady state at low Reynolds number as for Isotropic turbulence. Prandtl's secondary flow of the second kind does not occur for low Reynolds number flows, which qualitatively agrees with previous observetion in a mixing-box.

A practical demonstration of scalable, parallel mesh generation

Cambridge Flow Solutions Ltd, Compass House, Vision Park, Cambridge, CB4 9AD, UK Real-world simulation challenges are getting bigger: virtual aero-engines with multistage blade rows coupled with their secondary air systems & with fully featured geometry; environmental flows at meta-scales over resolved cities; synthetic battlefields. It is clear that the future of simulation is scalable, end-to-end parallelism. To address these challenges we have reported in a sequence of papers a series of inherently parallel building blocks based on the integration of a Level Set based geometry kernel with an octree-based cut-Cartesian mesh generator, RANS flow solver, post-processing and geometry management & editing. The cut-cells which characterize the approach are eliminated by exporting a body-conformal mesh driven by the underpinning Level Set and managed by mesh quality optimization algorithms; this permits third party flow solvers to be deployed. This paper continues this sequence by reporting & demonstrating two main novelties: variable depth volume mesh refinement enabling variable surface mesh refinement and a radical rework of the mesh generation into a bottom-up system based on Space Filling Curves. Also reported are the associated extensions to body-conformal mesh export. Everything is implemented in a scalable, parallel manner. As a practical demonstration, meshes of guaranteed quality are generated for a fully resolved, generic aircraft carrier geometry, a cooled disc brake assembly and a B747 in landing configuration. Copyright © 2009 by W.N.Dawes.

An experimental and numerical study of an oscillating transonic shock wave in a duct

A combined experimental and numerical study of a transonic shock wave in a parallel walled duct subject to downstream pressure perturbations has been conducted. Experiments and simulations have been carried out with a shock strength of M∞ = 1.4 for pressure perturbation frequencies in the range 16-90 Hz. The dynamics of unsteady shock motion and the interaction structure between the unsteady transonic shock wave and the turbulent tunnel floor boundary layer have been investigated. It is found that the (experimentally measured) dynamics of shock motion are generally well predicted by the computational scheme, especially at relatively low (≈ 40 Hz) frequencies. However, at higher frequencies (≈ 90 Hz), some subtle differences between the shock dynamics measured in experiments and those predicted by Computational Fluid Dynamics (CFD) exist. There is evidence from experiments that variations in shock / boundary layer interaction (SBLI) structure caused by shock motion are responsible for a change in the nature of shock dynamics between low and high frequency. In contrast, numerical results at low and high frequencies do not differ significantly and this suggests that the numerical method is not fully capturing the physics of the unsteady flow. Possible reasons for this are considered and a number of areas where CFD is unable to replicate experimental observations are identified. Significantly, CFD predicts changes in SBLI structure due to shock motion that are much too large and this may explain why none of the subtle effects on shock dynamics seen in experiments occur in CFD. Further work developing numerical methods that demonstrate a more realistic sensitivity of SBLI structure to unsteady shock motion is required. Copyright © 2010 by P.J.K. Bruce.

Numerical analysis of the current and voltage sharing issues for resistive fault current limiter using YBCO coated conductors

YBaCuO-coated conductors offer great potential in terms of performance and cost-saving for superconducting fault current limiter (SFCL). A resistive SFCL based on coated conductors can be made from several tapes connected in parallel or in series. Ideally, the current and voltage are shared uniformly by the tapes when quench occurs. However, due to the non-uniformity of property of the tapes and the relative positions of the tapes, the currents and the voltages of the tapes are different. In this paper, a numerical model is developed to investigate the current and voltage sharing problem for the resistive SFCL. This model is able to simulate the dynamic response of YBCO tapes in normal and quench conditions. Firstly, four tapes with different Jc 's and n values in E-J power law are connected in parallel to carry the fault current. The model demonstrates how the currents are distributed among the four tapes. These four tapes are then connected in series to withstand the line voltage. In this case, the model investigates the voltage sharing between the tapes. Several factors that would affect the process of quenches are discussed including the field dependency of Jc, the magnetic coupling between the tapes and the relative positions of the tapes. © 2010 IEEE.