Search results for "Stokes flow"

Permeability of three-dimensional random fiber webs

1998

We report the results of essentially ab initio simulations of creeping flow through large threedimensional random fiber webs that closely resemble fibrous sheets such as paper and nonwoven fabrics. The computational scheme used in this Letter is that of the lattice-Boltzmann method and contains no free parameters concerning the properties of the porous medium or the dynamics of the flow. The computed permeability of the web is found to be in good agreement with experimental data, and confirms that permeability depends exponentially on porosity over a large range of porosity. [S0031-9007(97)05087-4]

A Derivation of the Vlasov-Stokes System for Aerosol Flows from the Kinetic Theory of Binary Gas Mixtures

2016

In this short paper, we formally derive the thin spray equation for a steady Stokes gas, i.e. the equation consists in a coupling between a kinetic (Vlasov type) equation for the dispersed phase and a (steady) Stokes equation for the gas. Our starting point is a system of Boltzmann equations for a binary gas mixture. The derivation follows the procedure already outlined in [Bernard-Desvillettes-Golse-Ricci, arXiv:1608.00422 [math.AP]] where the evolution of the gas is governed by the Navier-Stokes equation.

An improved immersed boundary method for curvilinear grids

2009

Abstract In the present paper we propose an extension of the direct-forcing immersed boundary technique, recently developed and employed by Verzicco and co-authors [Fadlun EA, Verzicco R, Orlandi P, Mohd-Yusof J. Combined immersed-boundary finite-difference methods for three-dimensional complex flow simulations. J Comput Phys 2000;161:35–60; Verzicco R, Fatica M, Iaccarino G, Moin P, Khalighi B. Large eddy simulation of a road vehicle with drag-reduction devices. AIAA J 2002;40(12):2447–55; Cristallo A, Verzicco R. Combined immersed boundary/large-eddy-simulations of incompressible three-dimensional complex flows. Flow Turbul Combust 2006;77(1–4):3–26.] and successively improved by Balaras …

Frequency-dependent hydrodynamic interaction between two solid spheres

2017

Hydrodynamic interactions play an important role in many areas of soft matter science. In simulations with implicit solvent, various techniques such as Brownian or Stokesian dynamics explicitly include hydrodynamic interactions a posteriori by using hydrodynamic diffusion tensors derived from the Stokes equation. However, this equation assumes the interaction to be instantaneous which is an idealized approximation and only valid on long time scales. In the present paper, we go one step further and analyze the time-dependence of hydrodynamic interactions in a compressible fluid on the basis of the linearized Navier-Stokes equation. The theoretical results show that the compressibility of the…

Direct numerical simulations of creeping to early turbulent flow in unbaffled and baffled stirred tanks

2018

Abstract It has been known for a long time that the fluid flow and several global quantities, such as the power and pumping numbers, are about the same in baffled and unbaffled mechanically stirred vessels at low Reynolds numbers, but bifurcate at some intermediate Re and take drastically different values in fully turbulent flow. However, several details are not yet completely understood, notably concerning the relation of this bifurcation with the flow features and the transition to turbulence. In order to shed light on these issues, computational fluid dynamics was employed to predict the flow field in two vessels stirred by a six-bladed Rushton turbine at Reynolds numbers from 0.2 to 600…

Non-Local Scattering Kernel and the Hydrodynamic Limit

2007

In this paper we study the interaction of a fluid with a wall in the framework of the kinetic theory. We consider the possibility that the fluid molecules can penetrate the wall to be reflected by the inner layers of the wall. This results in a scattering kernel which is a non-local generalization of the classical Maxwell scattering kernel. The proposed scattering kernel satisfies a global mass conservation law and a generalized reciprocity relation. We study the hydrodynamic limit performing a Knudsen layer analysis, and derive a new class of (weakly) nonlocal boundary conditions to be imposed to the Navier-Stokes equations.

Zero Viscosity Limit for Analytic Solutions of the Navier-Stokes Equation on a Half-Space.¶ II. Construction of the Navier-Stokes Solution

1998

This is the second of two papers on the zero-viscosity limit for the incompressible Navier-Stokes equations in a half-space in either 2D or 3D. Under the assumption of analytic initial data, we construct solutions of Navier-Stokes for a short time which is independent of the viscosity. The Navier-Stokes solution is constructed through a composite asymptotic expansion involving the solutions of the Euler and Prandtl equations, which were constructed in the first paper, plus an error term. This shows that the Navier-Stokes solution goes to an Euler solution outside a boundary layer and to a solution of the Prandtl equations within the boundary layer. The error term is written as a sum of firs…

2020

Abstract. Quantifying the hydraulic properties of single fractures is a fundamental requirement to understand fluid flow in fractured reservoirs. For an ideal planar fracture, the effective flow is proportional to the cube of the fracture aperture. In contrast, real fractures are rarely planar, and correcting the cubic law in terms of fracture roughness has therefore been a subject of numerous studies in the past. Several empirical relationships between hydraulic and mechanical aperture have been proposed based on statistical variations of the aperture field. However, often, they exhibit non-unique solutions, attributed to the geometrical variety of naturally occurring fractures. In this st…

Effective slippage on superhydrophobic trapezoidal grooves

2013

We study the effective slippage on superhydrophobic grooves with trapezoidal cross-sections of various geometries (including the limiting cases of triangles and rectangular stripes), by using two complementary approaches. First, dissipative particle dynamics (DPD) simulations of a flow past such surfaces have been performed to validate an expression [E.S.Asmolov and O.I.Vinogradova, J. Fluid Mech. \textbf{706}, 108 (2012)] that relates the eigenvalues of the effective slip-length tensor for one-dimensional textures. Second, we propose theoretical estimates for the effective slip length and calculate it numerically by solving the Stokes equation based on a collocation method. The comparison …

Comparison of continuous and discontinuous Galerkin approaches for variable-viscosity Stokes flow

2015

We describe a Discontinuous Galerkin (DG) scheme for variable-viscosity Stokes flow which is a crucial aspect of many geophysical modelling applications and conduct numerical experiments with different elements comparing the DG approach to the standard Finite Element Method (FEM). We compare the divergence-conforming lowest-order Raviart-Thomas (RT0P0) and Brezzi-Douglas-Marini (BDM1P0) element in the DG scheme with the bilinear Q1P0 and biquadratic Q2P1 elements for velocity and their matching piecewise constant/linear elements for pressure in the standard continuous Galerkin (CG) scheme with respect to accuracy and memory usage in 2D benchmark setups. We find that for the chosen geodynami…