The bifurcations of penetrative Rayleigh-Benard convection in cylindrical containers are studied by the linear stability analysis (LSA) combined with the direct numerical simulation (DNS) method. The working fluid is cold water near 4 degrees C, where the Prandtl number Pr is 11.57, and the aspect ratio (radius/height) of the cylinder ranges from 0.66 to 2. It is found that the critical Rayleigh number increases with the increase in the density inversion parameter (m). The relationship between the normalized critical Rayleigh number (Ra-c((m))/Ra-c(0)) and (m) is formulated, which is in good agreement with the stability results within a large range of (m). The aspect ratio has a minor effect on Ra-c((m))/Ra-c(0). The bifurcation processes based on the axisymmetric solutions are also investigated. The results show that the onset of axisymmetric convection occurs through a trans-critical bifurcation due to the top-bottom symmetry breaking of the present system. Moreover, two kinds of qualitatively different steady axisymmetric solutions are identified.

In this paper, we will survey some recent results on the study of the viscous and invisid compressible flow with vacuum. It is wellknown that the study on vacuum has significance in the investigation on some important physical phenomena. However, most of the important questions about vacuum are still open due to the singularities caused by vacuum which need new mathematical tools and techniques to handle.

In this numerical study on Rayleigh-Benard convection, we seek to improve the heat transfer by passive means. To this end we introduce a single tilted conductive barrier centered in an aspect ratio one cell, breaking the symmetry of the geometry and to channel the ascending hot and descending cold plumes. We study the global and local heat transfer and the flow organization for Rayleigh numbers 10(5) <= Ra <= 10(9) for a fixed Prandtl number of Pr = 4.3. We find that the global heat transfer can be enhanced up to 18%, and locally around 800%. The averaged Reynolds number is always decreased when a barrier is introduced, even for those cases where the global heat transfer is increased. We map the entire parameter space spanned by the orientation and the size of a single barrier for Ra = 10(8).

This paper presents a numerical study of the Rayleigh-Benard convection (RBC) in two-dimensional cells with asymmetric (ratchet) roughness distributed on the top and bottom surfaces. We consider two aspect ratios of roughness gamma = 1, 2 and the range of the Rayleigh number 1.0 x 10(6) <= Ra <= 2.0 x 10(10) with the Prandtl number Pr = 4. The influences of the roughness on the heat transfer and the flow structure are found to be strongly dependent on both Ra and the roughness geometry. We find that the roughness can have a significant influence on the organization of the secondary corner rolls, and the corner rolls are evidently suppressed by the roughness for intermediate values of Ra. In the presence of the roughness, a sharp jump of the Nu values is identified as the Ra value is slightly increased, accompanied with the dramatic changes of the large-scale flow structure and the plume dynamics. The influences of the ratchet orientation on the heat transfer and the flow structure are discussed and analyzed.

In this paper, we propose a rigorous and accurate non-local (in the oversampled region) upscaling framework based on some recently developed multiscale methods [10]. Our proposed method consists of identifying multi-continua parameters via local basis functions and constructing non-local (in the oversampled region) transfer and effective properties. To achieve this, we significantly modify our recent work proposed within Generalized Multiscale Finite Element Method (GMsFEM) in [10] and derive appropriate local problems in oversampled regions once we identify important modes representing each continuum. We use piecewise constant functions in each fracture network and in the matrix to write an upscaled equation. Thus, the resulting upscaled equation is of minimal size and the unknowns are average pressures in the fractures and the matrix. Note that the use of non-local upscaled model for porous

We introduce a unified particle framework which integrates the phase-field method with multi-material simulation to allow modeling of both liquids and solids, as well as phase transitions between them. A simple elastoplastic model is used to capture the behavior of various kinds of solids, including deformable bodies, granular materials, and cohesive soils. States of matter or phases, particularly liquids and solids, are modeled using the non-conservative Allen-Cahn equation. In contrast, materials—made of different substances—are advected by the conservative Cahn-Hilliard equation. The distributions of phases and materials are represented by a phase variable and a concentration variable, respectively, allowing us to represent commonly observed fluid-solid interactions. Our multi-phase, multi-material system is governed by a unified Helmholtz free energy density. This framework provides the first method in computer graphics capable of modeling a continuous interface between phases. It is versatile and can be readily used in many scenarios that are challenging to simulate. Examples are provided to demonstrate the capabilities and effectiveness of this approach.

We study homogenization of the G-equation with a flow straining term (or the strain G-equation) in two dimensional periodic cellular flow. The strain G-equation is a highly non-coercive and non-convex level set HamiltonJacobi equation. The main objective is to investigate how the flow induced straining (the nonconvex term) influences front propagation as the flow intensity <i>A</i> increases. Three distinct regimes are identified. When <i>A</i> is below the critical level, homogenization holds and the turbulent flame speed <i>s</i> _T (effective Hamiltonian) is well-defined for any periodic flow with small divergence and is enhanced by the cellular flow as <i>s</i> _T <i>O</i>(<i>A</i>/log <i>A</i>). In the second regime where <i>A</i> is slightly above the critical value, homogenization breaks down, and <i>s</i> _T is not well-defined along any direction. Solutions become a mixture of a fast moving part and a stagnant part. When <i>A</i> is

The minimal speeds (c) of the KolmogorovPetrovskyPiskunov (KPP) fronts at small diffusion ( 1) in a class of time-periodic cellular flows with chaotic streamlines is investigated in this paper. The variational principle of c reduces the computation to that of a principle eigenvalue problem on a periodic domain of a linear advectiondiffusion operator with spacetime periodic coefficients and small diffusion. To solve the advection dominated time-dependent eigenvalue problem efficiently over large time, a combination of spectral methods and finite element, as well as the associated fast solvers, are utilized to accelerate computation. In contrast to the scaling c= O ( 1/4) in steady cellular flows, a new relation c= O (1) as 1 is revealed in the time-periodic cellular flows due to the presence of chaotic streamlines. Residual propagation speed emerges from the Lagrangian chaos which is quantified as a sub

The paper aims to estimate the thickness of the boundary layer for the planar MHD system with vanishing shear viscosity . Under some conditions on the initial and boundary data, we show that the thickness is of the order | In |. Note that this estimate holds also for the Navier-Stokes system so that it extends the previous works even without the magnetic effect.

We study the two-point correlation function of a freely decaying scalar in Kraichnan's model of advection by a Gaussian random velocity field that is stationary and white noise in time, but fractional Brownian in space with roughness exponent 0&lt;<i></i>&lt;2, appropriate to the inertial-convective range of the scalar. We find all self-similar solutions by transforming the scaling equation to Kummer's equation. It is shown that only those scaling solutions with scalar energy decay exponent <i>a</i>(<i>d</i>/<i></i>)+1 are statistically realizable, where <i>d</i> is space dimension and <i></i>=2<i></i>. An infinite sequence of invariants <i>J</i> _p, <i>p</i>=0,1,2,..., is pointed out, where <i>J</i> ₀ is Corrsin's integral invariant but the higher invariants appear to be new. We show that at least one of the invariants <i>J</i> ₀ or <i>J</i> ₁ must be nonzero (possibly infinite) for realizable initial data. Initial datum with a finite, nonzero invariantthe first being <i>J</i> _pconverges at long times to a scaling