Implicit-explicit Runge–Kutta schemes and finite elements with symmetric stabilization for advection-diffusion equations

We analyze a two-stage implicit-explicit Runge–Kutta scheme for time discretization of advection-diffusion equations. Space discretization uses continuous, piecewise affine finite elements with interelement gradient jump penalty; discontinuous Galerkin methods can be considered as well. The advective and stabilization operators are treated explicitly, whereas the diffusion operator is treated implicitly. Our analysis hinges on L 2 -energy estimates on discrete functions in physical space. Our main results are stability and quasi-optimal error estimates for smooth solutions under a standard hyperbolic CFL restriction on the time step, both in the advection-dominated and in the diffusion-dominated regimes. The theory is illustrated by numerical examples

Analysis of Compatible Discrete Operator Schemes for the Stokes Equations on Polyhedral Meshes

Compatible Discrete Operator schemes preserve basic properties of the continuous model at the discrete level. They combine discrete differential operators that discretize exactly topological laws and discrete Hodge operators that approximate constitutive relations. We devise and analyze two families of such schemes for the Stokes equations in curl formulation, with the pressure degrees of freedom located at either mesh vertices or cells. The schemes ensure local mass and momentum conservation. We prove discrete stability by establishing novel discrete Poincar\'e inequalities. Using commutators related to the consistency error, we derive error estimates with first-order convergence rates for smooth solutions. We analyze two strategies for discretizing the external load, so as to deliver tight error estimates when the external load has a large irrotational or divergence-free part. Finally, numerical results are presented on three-dimensional polyhedral meshes

Interaction and coalescence of large bubbles rising in a thin gap

We present accurate measurements of the relative motion and deformation of two large bubbles released consecutively in a quiescent liquid confined in a thin-gap cell. Although the second injected bubble was smaller, we observed that, in all cases, it accelerated and caught up with the leading bubble. This acceleration is related to the wake of the leading bubble, which also induces significant changes in the width and curvature of the trailing bubble. On the contrary, the velocity of the leading bubble is unaltered during the whole interaction and coalescence process. Shape adaptation of the two bubbles is observed just prior to coalescence. After pinch-off, the liquid film is drained at a constant velocity

Equilibrated tractions for the Hybrid High-Order method

We show how to recover equilibrated face tractions for the hybrid high-order method for linear elasticity recently introduced in [D. A. Di Pietro and A. Ern, A hybrid high-order locking-free method for linear elasticity on general meshes, Comput. Meth. Appl. Mech. Engrg., 2015, 283:1-21], and prove that these tractions are optimally convergent

The motion of an axisymmetric body falling in a tube at moderate Reynolds numbers

This study concerns the rectilinear and periodic paths of an axisymmetric solid body (short-length cylinder and disk of diameter d and thickness h) falling in a vertical tube of diameter D. We investigated experimentally the influence of the confinement ratio (S=d/D<0.8) on the motion of the body, for different aspect ratios (χ=d/h=3, 6 and 10), Reynolds numbers (80<Re<320) and a density ratio between the fluid and the body close to unity. For a given body, the Reynolds number based on its mean vertical velocity is observed to decrease when S increases. The critical Reynolds number for the onset of the periodic motion decreases with S in the case of thin bodies (χ=10), whereas it appears unaffected by S for thicker bodies (χ=3 and 6). The characteristics of the periodic motion are also strongly modified by the confinement ratio. A thick body (χ=3) tends to go back to a rectilinear path when S increases, while a thin body (χ=10) displays oscillations of growing amplitude with S until it touches the tube (at about S=0.5). For a given aspect ratio, however, the amplitudes of the oscillations follow a unique curve for all S, which depends only on the relative distance of the Reynolds number to the threshold of path instability. In parallel, numerical simulations of the wake of a body held fixed in a uniform confined flow were carried out. The simulations allowed us to determine in this configuration the effect of the confinement ratio on the thresholds for wake instability (loss of axial symmetry at Rec₁ and loss of stationarity at Rec₂) and on the maximal velocity Vw in the recirculating region of the stationary axisymmetric wake. The evolution with χ and S of Vw at Rec₁ was used to define a Reynolds number Re*. Remarkably, for a freely moving body, Re* remains almost constant when S varies, regardless of the nature of the path

Motion of a single bubble rising in a countercurrent flow in a Hele-Shaw cell

We investigate experimentally the motion of isolated bubbles rising in a vertical Hele-Shaw cell in the presence of a downward flow. The bubbles are strongly flattened in the plane of the cell, their equivalent diameter d being large compared to the gap of the cell e . Furthermore, their dynamics is strongly influenced by the confinement which imposes thin liquid films between the bubble and the walls and strongly attenuates the flow perturbation in the liquid due to wall friction

Mollification in strongly Lipschitz domains with application to continuous and discrete De Rham complex

We construct mollification operators in strongly Lipschitz domains that do not invoke non-trivial extensions, are $L^p$ stable for any real number $p\in[1,\infty]$, and commute with the differential operators $\nabla$, $\nabla{\times}$, and $\nabla{\cdot}$. We also construct mollification operators satisfying boundary conditions and use them to characterize the kernel of traces related to the tangential and normal trace of vector fields. We use the mollification operators to build projection operators onto general $H^1$-, $\mathbf{H}(\text{curl})$- and $\mathbf{H}(\text{div})$-conforming finite element spaces, with and without homogeneous boundary conditions. These operators commute with the differential operators $\nabla$, $\nabla{\times}$, and $\nabla{\cdot}$, are $L^p$-stable, and have optimal approximation properties on smooth functions

A study on schedule management for BIM projects in the construction industry

There is an advance modelling tool that currently been pushed by the industry is BIM. BIM as known as Building Modelling Information is a computerized process that is used to design, understand and establish the key physical and functional characteristic of a building on a ‘virtual’ computerized model basis at its most basic level [4]. Basically the resulting model is a digital representation of the building which the data can be extracted and analyzed to generate information that can be used for decision making and enhance the process of delivering the building and the entire life cycle use of the building [4]. BIM implementation can help to improve the quality of project especially the schedule management. By implementing BIM into construction project, it can provides schedule visualization which can make the construction planning more efficient. Besides that, through the BIM model clash detection can be detected in the preconstruction phase which save a lot of time on rework during construction phase