The Experts below are selected from a list of 24 Experts worldwide ranked by ideXlab platform
Peter Hansbo - One of the best experts on this subject based on the ideXlab platform.
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application of a minimal compatible element to Incompressible and nearly Incompressible Continuum mechanics
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Erik Burman, Snorre H Christiansen, Peter HansboAbstract:Abstract In this note we will explore some applications of the recently constructed piecewise affine, H 1 -conforming element that fits in a discrete de Rham complex (Christiansen and Hu, 2018). In particular we show how the element leads to locking free methods for Incompressible elasticity and viscosity robust methods for the Brinkman model.
Erik Burman - One of the best experts on this subject based on the ideXlab platform.
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application of a minimal compatible element to Incompressible and nearly Incompressible Continuum mechanics
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Erik Burman, Snorre H Christiansen, Peter HansboAbstract:Abstract In this note we will explore some applications of the recently constructed piecewise affine, H 1 -conforming element that fits in a discrete de Rham complex (Christiansen and Hu, 2018). In particular we show how the element leads to locking free methods for Incompressible elasticity and viscosity robust methods for the Brinkman model.
Snorre H Christiansen - One of the best experts on this subject based on the ideXlab platform.
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application of a minimal compatible element to Incompressible and nearly Incompressible Continuum mechanics
Computer Methods in Applied Mechanics and Engineering, 2020Co-Authors: Erik Burman, Snorre H Christiansen, Peter HansboAbstract:Abstract In this note we will explore some applications of the recently constructed piecewise affine, H 1 -conforming element that fits in a discrete de Rham complex (Christiansen and Hu, 2018). In particular we show how the element leads to locking free methods for Incompressible elasticity and viscosity robust methods for the Brinkman model.
David R Emerson - One of the best experts on this subject based on the ideXlab platform.
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non equilibrium effects on flow past a circular cylinder in the slip and early transition regime
Journal of Fluid Mechanics, 2019Co-Authors: Robert W Barber, Benzi John, David R EmersonAbstract:This paper presents a comprehensive investigation into flow past a circular cylinder where compressibility and rarefaction effects play an important role. The study focuses on steady subsonic flow in the Reynolds-number range 0.1–45. Rarefaction, or non-equilibrium, effects in the slip and early transition regime are accounted for using the method of moments and results are compared to data from kinetic theory obtained from the direct simulation Monte Carlo method. Solutions obtained for Incompressible Continuum flow serve as a baseline to examine non-equilibrium effects on the flow features. For creeping flow, where the Reynolds number is less than unity, the drag coefficient predicted by the moment equations is in good agreement with kinetic theory for Knudsen numbers less than one. When flow separation occurs, we show that the effects of rarefaction and velocity slip delay flow separation and will reduce the size of the vortices downstream of the cylinder. When the Knudsen number is above 0.028, the vortex length shows an initial increase with the Reynolds number, as observed in the standard no-slip Continuum regime. However, once the Reynolds number exceeds a critical value, the size of the downstream vortices decreases with increasing Reynolds number until they disappear. An existence criterion, which identifies the limits for the presence of the vortices, is proposed. The flow physics around the cylinder is further analysed in terms of velocity slip, pressure and skin friction coefficients, which highlights that viscous, rarefaction and compressibility effects all play a complex role. We also show that the local Knudsen number, which indicates the state of the gas around the cylinder, can differ significantly from its free-stream value and it is essential that computational studies of subsonic gas flows in the slip and early transition regime are able to account for these strong non-equilibrium effects.
Donald L Koch - One of the best experts on this subject based on the ideXlab platform.
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collision and rebound of small droplets in an Incompressible Continuum gas
Journal of Fluid Mechanics, 2002Co-Authors: Arvind Gopinath, Donald L KochAbstract:We study the head-on collision between two weakly deformable droplets, each of radius a (in the range 10-150 μm), moving towards one another with characteristic impact speeds ±U' c . The liquid comprising the drop has density ρ d and viscosity μ d . The collision takes place in an Incompressible Continuum gas with ambient density ρ g « ρ d , ambient pressure p' ∞ and viscosity μ g « μ d . The gas-liquid interface is surfactant free with interfacial tension a. The Weber number based on the drop density, We d ≡ ρ d U' 2 c a/σ « 1 and the capillary number based on the gas viscosity, Cα g ≡ μ g U' c /σ « 1. The Reynolds number characterizing flow inside the drops satisfies Re d ≡ aU' c ρ d /μ d » We 1/2 d and the Stokes number characterizing the drop inertia, St ≡ 2We d (9Ca g ) -1 = 2(ρ d U' c aμ -1 g )/9 is O(1) or larger. We first analyse a simple model for the rebound process which is valid when St » 1 and viscous dissipation in both the gas and in the drop can be neglected. We assume that the film separating the drops only serves to keep the interfaces from touching by supplying a constant excess pressure 2σ/a. A singular perturbation analysis reveals that when ln(We -1/4 d ) » 1, rebound occurs on a time scale t' b = 2 3 1/2 πaWe 1/2 d ln 1/2 (We -1/4 d )U' -1 c . Numerical results for Weber numbers in the range O(10 -6 ) - O(10 -1 ) compare very well to existing experimental and simulation results, indicating that the approximate treatment of the bounce process is applicable for We d < 0.3. In the second part of the paper we formulate a general theory that not only models the flow inside the drop but also takes into account the evolution of the gap width separating the drops. The drop deformation in the near-contact inner region is determined by solving the lubrication equations and matching to an outer solution. The resulting equations are solved numerically using a direct, semi-implicit, matrix inversion technique for capillary numbers in the range 10 -8 to 10 -4 and Stokes numbers from 2 to 200. Trajectories are mapped out in terms of Ca g and the parameter % = (We d /Ca g ) 1/2 so that St ≡ 2 9Χ 2 . For small Stokes numbers, the drops behave as nearly rigid spheres and come to rest without any significant rebound. For O(1) Stokes numbers, the surfaces deform noticeably and a dimple forms when the gap thickness is approximately O(aCa 1/2 g ). The dimple extent increases, reaches a maximum and then decreases to zero. Meanwhile, the centroids of the two drops come to rest momentarily and then the drops rebound, executing oscillatory motions before finally coming to rest. As the Stokes number increases with Ca g held fixed, more energy is stored as deformation energy and the maximum radial extent of the dimple increases accordingly. For St » 1, no oscillations in the centroid positions are observed, but the temporal evolution of the minimum gap thickness exhibits two minima. One minimum occurs during the dimple evolution process and corresponds to the minimum attained by the dimple rim. The second minimum occurs along the axis of symmetry when the dimple relaxes, a tail forms and then retracts. A detailed analysis of the interface shapes, pressure profiles and the force acting on the drops allows us to obtain a complete picture of the collision and rebound process.
