The influences of non-Oberbeck-Boussinesq (NOB) effects on flow instabilities and bifurcation characteristics of Rayleigh-Benard convection are examined. The working fluid is air with reference Prandtl number Pr = 0.71 and contained in two-dimensional rigid cavities of finite aspect ratios. The fluid flow is governed by the low-Mach-number equations, accounting for the NOB effects due to large temperature difference involving flow compressibility and variations of fluid viscosity and thermal conductivity with temperature. The intensity of NOB effects is measured by the dimensionless temperature differential epsilon. Linear stability analysis of the thermal conduction state is performed. An epsilon(2) scaling of the leading-order corrections of critical Rayleigh number Ra-cr and disturbance growth rate sigma due to NOB effects is identified, which is a consequence of an intrinsic symmetry of the system. The influences of weak NOB effects on flow instabilities are further studied by perturbation expansion of linear stability equations with regard to epsilon, and then the influence of aspect ratio A is investigated in detail. NOB effects are found to enhance (weaken) flow stability in large (narrow) cavities. Detailed contributions of compressibility, viscosity and buoyancy actions on disturbance kinetic energy growth are identified quantitatively by energy analysis. Besides, a weakly nonlinear theory is developed based on centre-manifold reduction to investigate the NOB influences on bifurcation characteristics near convection onset, and amplitude equations are constructed for both codimension-one and -two cases. Rich bifurcation regimes are observed based on amplitude equations and also confirmed by direct numerical simulation. Weakly nonlinear analysis is useful for organizing and understanding these simulation results.

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

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

We develop an efficient numerical method to compute single slit or double slit diffraction patterns from high frequency wave in inhomogeneous media. We approximate the high frequency asymptotic solution to the Helmholtz equation using the Eulerian Gaussian beam summation proposed in [20, 21]. The emitted rays from a slit are embedded in the phase space using an open segment. The evolution of this open curve is accurately computed using the recently developed Grid Based Particle Method [24] which results in a very efficient computational algorithm. Following the grid based particle method we proposed in [23, 24], we represent the open curve or the open surface by meshless Lagrangian particles sampled according to an underlying fixed Eulerian mesh. The end-points of the open curve are tracked explicitly and consistently with interior particles. To construct the overall wavefield, each of these sampling particles also carry necessary quantities that are obtained by solving advection-reaction equations. Numerical experiments show that the resulting method can model diffraction patterns in inhomogeneous media accurately, even in the occurrence of caustics.

Multiple-fluid interaction is an interesting and common visual phenomenon we often observe. In this paper we present an energybased Lagrangian method that expands the capability of existing multiple-fluid methods to handle various phenomena, including extraction, partial dissolution, etc. Based on our user-adjusted Helmholtz free energy functions, the simulated fluid evolves from high-energy states to low-energy states, allowing flexible capture of various mixing and unmixing processes. We also extend the original Cahn-Hilliard equation to gain abilities of simulating complex fluid-fluid interaction and rich visual phenomena such as motionrelated mixing and position based pattern. Our approach is easy to be integrated with existing state-of-the-art smooth particle hydrodynamic (SPH) solvers and can be further implemented on top of the position based dynamics (PBD) method, improving the stability and incompressibility of the fluid during Lagrangian simulation under large time steps. Performance analysis shows that our method is at least 4 times faster than the state-of-the-art multiple-fluid method. Examples are provided to demonstrate the new capability and effectiveness of our approach.