We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduc...
We introduce a lattice Boltzmann model for simulating immiscible binary fluids in two dimensions. The model, based on the Boltzmann equation of lattice-gas hydrodynamics, incorporates features of a previously introduced discrete immiscible lattice-gas model. A theoretical value of the surface-tension coefficient is derived and found to be in excellent agreement with values obtained from simulations. The model serves as a numerical method for the simulation of immiscible two-phase flow; a preliminary application illustrates a simulation of flow in a two-dimensional microscopic model of a porous medium. Extension of the model to three dimensions appears straightforward.
The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional general...
The dynamical triangulation model of 3-dimensional Quantum Gravity is defined and studied. We propose two different algorithms for numerical simulations, leading to consistent results. One is the 3-dimensional generalization of the bonds flip, another is more sophisticated algorithm, based on Schwinger–Dyson equations. We found such care necessary, because our results appear to be quite unexpected. We simulated up to 60000 tetrahedra and observed none of the feared pathologies like factorial growth of the partition function with volume, or collapse to the branched polymer phase. The volume of the Universe grows exponentially when the bare cosmological constant λ approaches the critical value λ c from above, but the closed Universe exists and has peculiar continuum limit. The Universe compressibility diverges as (λ − λ c ) −2 and the bare Newton constant linearly approaches negative critical value as λ goes to λ c , provided the average curvature is kept at zero. The fractal properties turned out to be the same, as in two dimensions, namely the effective Hausdorff dimension grows logarithmically with the size of the test geodesic sphere.
The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discret...
The response of transport measures (Nusselt number, drag and lift force) for two- and three-dimensional flow past a heated cylinder reaching a chaotic state is investigated numerically using a spectral element discretization at a Reynolds number Re = 500. The undisturbed two-dimensional flow remains periodic at this Reynolds number, unless a suitable forcing is applied on the naturally produced system. Three-dimensional simulations establish that three-dimensionality sets in at Re almost-equal-to 200. Successive supercritical states are established through a series of period-doublings, before a chaotic state is reached at a Re almost-equal-to 500. For the two-dimensional forced flow, all transport measures oscillate aperiodically in time and undergo a "crisis," i.e., a sudden and dramatic increase in their amplitude. The corresponding three-dimensional, naturally produced chaotic state corresponds to a less drastic change of the transport quantities with both rms and mean values lower than their two-dimensional counterparts.
It has been observed, in earlier computations of bifurcation diagrams for dissipative partial differential equations, that the use of certain explicit approximate inertial forms can give rise to numerical artifacts su...
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Turbulence, a problem of classical macroscopic physics, has received renewed attention of late as a subject whose understanding can shed light on the fundamental physical laws governing systems. Turbulent fluid motion...
Turbulence, a problem of classical macroscopic physics, has received renewed attention of late as a subject whose understanding can shed light on the fundamental physical laws governing systems. Turbulent fluid motion exhibits such a higher degree of complexity and unpredictability that it has been considered essentially random. On the other hand, experimental evidence suggests that a remarkable degree of coherence is also present. It is precisely this subtle mixture of order and disorder that lies at heart of the difficulty in achieving a comprehensive theoretical description. While some analytical approaches have succeeded in describing the mean properties of the disorder, the lack of a characterization of key dynamic and static features of the coherence (structures) has prevented a deep understanding of physical processes involved in turbulence dynamics.
The evolution of a randomly perturbed interface between unbounded incompressible fluids undergoing Rayleigh–Taylor instability is analyzed numerically and theoretically. Two‐dimensional simulation results, obtained ...
The evolution of a randomly perturbed interface between unbounded incompressible fluids undergoing Rayleigh–Taylor instability is analyzed numerically and theoretically. Two‐dimensional simulation results, obtained with an interface tracking code, are presented and compared with a theoretical model based on Young’s two‐phase flow description of the mixing process. The simplifications implied by self‐similarity and by high drag enable simple analytic results to be obtained for the profiles of the average volume fractions and velocities of the two materials as a function of penetration depth. Agreement of the analytic results with the simulation data is demonstrated for a wide range of density ratios.
We present a fast numerical method for solving the incompressible Euler's equation in two dimensions for the special case when the flow field can be represented by patches of constant vorticity. The method is an a...
We present a fast numerical method for solving the incompressible Euler's equation in two dimensions for the special case when the flow field can be represented by patches of constant vorticity. The method is an adaptive vortex method in which cells (vortex blobs) of multiple scales are used to represent the patches so that the number of vortex blobs needed to approximate the patches is proportional to the length of the boundary curve of the patch and inversely proportional to the width of the smallest blob (cell) used. Points along the boundaries of the patches are advected according to the velocity obtained from the approximating vortices.
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