35,569 research outputs found

    Pore-scale Modeling of Viscous Flow and Induced Forces in Dense Sphere Packings

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    We propose a method for effectively upscaling incompressible viscous flow in large random polydispersed sphere packings: the emphasis of this method is on the determination of the forces applied on the solid particles by the fluid. Pore bodies and their connections are defined locally through a regular Delaunay triangulation of the packings. Viscous flow equations are upscaled at the pore level, and approximated with a finite volume numerical scheme. We compare numerical simulations of the proposed method to detailed finite element (FEM) simulations of the Stokes equations for assemblies of 8 to 200 spheres. A good agreement is found both in terms of forces exerted on the solid particles and effective permeability coefficients

    Parallel TREE code for two-component ultracold plasma analysis

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    The TREE method has been widely used for long-range interaction {\it N}-body problems. We have developed a parallel TREE code for two-component classical plasmas with open boundary conditions and highly non-uniform charge distributions. The program efficiently handles millions of particles evolved over long relaxation times requiring millions of time steps. Appropriate domain decomposition and dynamic data management were employed, and large-scale parallel processing was achieved using an intermediate level of granularity of domain decomposition and ghost TREE communication. Even though the computational load is not fully distributed in fine grains, high parallel efficiency was achieved for ultracold plasma systems of charged particles. As an application, we performed simulations of an ultracold neutral plasma with a half million particles and a half million time steps. For the long temporal trajectories of relaxation between heavy ions and light electrons, large configurations of ultracold plasmas can now be investigated, which was not possible in past studies

    A hybrid method for hydrodynamic-kinetic flow - Part I -A particle-gridmethod for reducing stochastic noise in kinetic regimes

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    In this work we present a hybrid particle-grid Monte Carlo method for the Boltzmann equation, which is characterized by a significant reduction of the stochastic noise in the kinetic regime. The hybrid method is based on a first order splitting in time to separate the transport from the relaxation step. The transport step is solved by a deterministic scheme, while a hybrid DSMC-based method is used to solve the collision step. Such a hybrid scheme is based on splitting the solution in a collisional and a non-collisional part at the beginning of the collision step, and the DSMC method is used to solve the relaxation step for the collisional part of the solution only. This is accomplished by sampling only the fraction of particles candidate for collisions from the collisional part of the solution, performing collisions as in a standard DSMC method, and then projecting the particles back onto a velocity grid to compute a piecewise constant reconstruction for the collisional part of the solution. The latter is added to a piecewise constant reconstruction of the non-collisional part of the solution, which in fact remains unchanged during the relaxation step. Numerical results show that the stochastic noise is significantly reduced at large Knudsen numbers with respect to the standard DSMC method. Indeed in this algorithm, the particle scheme is applied only on the collisional part of the solution, so only this fraction of the solution is affected by stochastic fluctuations. But since the collisional part of the solution reduces as the Knudsen number increases, stochastic noise reduces as well at large Knudsen number

    Real-time separation of non-stationary sound fields on spheres

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    The sound field separation methods can separate the target field from the interfering noises, facilitating the study of the acoustic characteristics of the target source, which is placed in a noisy environment. However, most of the existing sound field separation methods are derived in the frequency-domain, thus are best suited for separating stationary sound fields. In this paper, a time-domain sound field separation method is developed that can separate the non-stationary sound field generated by the target source over a sphere in real-time. A spherical array sets up a boundary between the target source and the interfering sources, such that the outgoing field on the array is only generated by the target source. The proposed method decomposes the pressure and the radial particle velocity measured by the array into spherical harmonics coefficients, and recoveries the target outgoing field based on the time-domain relationship between the decomposition coefficients and the theoretically derived spatial filter responses. Simulations show the proposed method can separate non-stationary sound fields both in free field and room environments, and over a longer duration with small errors. The proposed method could serve as a foundation for developing future time-domain spatial sound field manipulation algorithms.Comment: 34 pages, 15 figure

    Improved procedure for the computation of Lamb's coefficients in the Physalis method for particle simulation

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    The Physalis method is suitable for the simulation of flows with suspended spherical particles. It differs from standard immersed boundary methods due to the use of a local spectral representation of the solution in the neighborhood of each particle, which is used to bridge the gap between the particle surface and the underlying fixed Cartesian grid. This analytic solution involves coefficients which are determined by matching with the finite-difference solution farther away from the particle. In the original implementation of the method this step was executed by solving an over-determined linear system via the singular-value decomposition. Here a more efficient method to achieve the same end is described. The basic idea is to use scalar products of the finite-difference solutions with spherical harmonic functions taken over a spherical surface concentric with the particle. The new approach is tested on a number of examples and is found to posses a comparable accuracy to the original one, but to be significantly faster and to require less memory. An unusual test case that we describe demonstrates the accuracy with which the method conserves the fluid angular momentum in the case of a rotating particle

    Fast Ewald summation for free-space Stokes potentials

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    We present a spectrally accurate method for the rapid evaluation of free-space Stokes potentials, i.e. sums involving a large number of free space Green's functions. We consider sums involving stokeslets, stresslets and rotlets that appear in boundary integral methods and potential methods for solving Stokes equations. The method combines the framework of the Spectral Ewald method for periodic problems, with a very recent approach to solving the free-space harmonic and biharmonic equations using fast Fourier transforms (FFTs) on a uniform grid. Convolution with a truncated Gaussian function is used to place point sources on a grid. With precomputation of a scalar grid quantity that does not depend on these sources, the amount of oversampling of the grids with Gaussians can be kept at a factor of two, the minimum for aperiodic convolutions by FFTs. The resulting algorithm has a computational complexity of O(N log N) for problems with N sources and targets. Comparison is made with a fast multipole method (FMM) to show that the performance of the new method is competitive.Comment: 35 pages, 15 figure
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