Search results for "Stokes flow"

High-order simulation scheme for active particles driven by stress boundary conditions

2020

Abstract We study the dynamics and interactions of elliptic active particles in a two dimensional solvent. The particles are self-propelled through prescribing a fluid stress at one half of the fluid-particle boundary. The fluid is treated explicitly solving the Stokes equation through a discontinuous Galerkin scheme, which allows to simulate strictly incompressible fluids. We present numerical results for a single particle and give an outlook on how to treat suspensions of interacting active particles.

Shape optimization for Stokes problem with threshold slip boundary conditions

2017

This paper deals with shape optimization of systems governed by the Stokes flow with threshold slip boundary conditions. The stability of solutions to the state problem with respect to a class of domains is studied. For computational purposes the slip term and impermeability condition are handled by a regularization. To get a finite dimensional optimization problem, the optimized part of the boundary is described by B´ezier polynomials. Numerical examples illustrate the computational efficiency. peerReviewed

Investigating the effects of intersection flow localization in equivalent-continuum-based upscaling of flow in discrete fracture networks

2021

Abstract. Predicting effective permeabilities of fractured rock masses is a crucial component of reservoir modeling. Its often realized with the discrete fracture network (DFN) method, whereby single-phase incompressible fluid flow is modeled in discrete representations of individual fractures in a network. Depending on the overall number of fractures, this can result in high computational costs. Equivalent continuum models (ECMs) provide an alternative approach by subdividing the fracture network into a grid of continuous medium cells, over which hydraulic properties are averaged for fluid flow simulations. While continuum methods have the advantage of lower computational costs and the pos…

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…

Fully developed laminar flow and heat transfer in serpentine pipes

2015

Abstract A serpentine pipe is a sequence of parallel straight pipe segments connected by U-bends. Its geometry is fully characterized by pipe radius, a , bend curvature radius, c and length of the straight segments, l . The repeated curvature inversion forces the recirculation (secondary flow) pattern to switch between two specular configurations, which may enhance mixing and heat or mass transfer with respect to a constant-curvature pipe at the cost of an increase in pressure drop. In the present work, fully developed laminar flow and heat transfer in serpentine pipes were investigated by numerical simulation. The curvature δ  =  a / c was made to vary between 0.1 and 0.5 while the paramet…

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…

Bending of ferrofluid droplet in rotating magnetic field

1999

Abstract This paper presents results concerning 2D ferrofluid droplet motion at high values of magnetic field and frequencies above a critical one with respect to droplet ability to follow field rotation. The boundary element method is used to solve 2D equations of a magnetic field and Stokes flow problems. If the viscosity of the ferrofluid is larger than that of the surrounding fluid, droplet exhibits bending, forming “S-shape”. Fluid flow inside the droplet is analyzed and the main stages of periodical rotation of a droplet are reported.

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…

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…