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  • 1. Bartuschat, D.
    et al.
    Fischermeier, E.
    Gustavsson, Katarina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Rüde, U.
    Two computational models for simulating the tumbling motion of elongated particles in fluids2016In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 127, p. 17-35Article in journal (Refereed)
    Abstract [en]

    Suspensions with fiber-like particles in the low Reynolds number regime are modeled by two different approaches that both use a Lagrangian representation of individual particles. The first method is the well-established formulation based on Stokes flow that is formulated as integral equations. It uses a slender body approximation for the fibers to represent the interaction between them directly without explicitly computing the flow field. The second is a new technique using the 3D lattice Boltzmann method on parallel supercomputers. Here the flow computation is coupled to a computational model of the dynamics of rigid bodies using fluid-structure interaction techniques. Both methods can be applied to simulate fibers in fluid flow. They are carefully validated and compared against each other, exposing systematically their strengths and weaknesses regarding their accuracy, the computational cost, and possible model extensions.

  • 2.
    Gustavsson, Katarina
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Oppelstrup, Jesper
    Consolidation of concentrated suspensions - numerical simulations using a two-phase fluid model2000In: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 3, p. 39-45Article in journal (Refereed)
  • 3.
    Gustavsson, Katarina
    et al.
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA.
    Oppelstrup, Jesper
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Numerical 2D models of consolidation of dense flocculated suspensions2001In: Journal of Engineering Mathematics, ISSN 0022-0833, E-ISSN 1573-2703, Vol. 41, no 2-3, p. 189-201Article in journal (Refereed)
    Abstract [en]

    A mathematical 2D model for a consolidation process of a highly concentrated, flocculated suspension is developed. The suspension is treated as a mixture of a fluid and solid particles by an Eulerian two-phase fluid model. The suspension is characterized by constitutive relations correlating the stresses, interaction forces, and inter-particle forces to concentration and velocity gradients. This results in three empirical material functions: a permeability, a non-Newtonian viscosity and a non-reversible particle interaction pressure. Parameters in the models are fitted to experimental data. A simulation program using finite difference methods both in time and space is applied to one and two dimensional test cases. The effect of different viscosity models as well as the effect of shear on consolidation rate is studied. The results show that a shear thinning viscosity model yields a higher consolidation rate compared to a model that only depends on the volume fraction. It is also concluded that the size of the viscosity influences the time scale of the process and that the expected effect of shear on the process is not weil reproduced with any of the models.

  • 4.
    Gustavsson, Katarina
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30).
    Oppelstrup, Jesper
    Eiken, Jon
    Consolidation of concentrated suspensions - shear and irreversible floc structure rearrangement2001In: Computing and Visualization in Science, ISSN 1432-9360, E-ISSN 1433-0369, Vol. 4, p. 61-66Article in journal (Refereed)
  • 5.
    Gustavsson, Katarina
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Tornberg, Anna Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Numerical Simulations of Rigid Fiber Suspensions2008Conference paper (Refereed)
    Abstract [en]

    In this paper, we present a numerical method designed to simulate the

    challenging problem of the dynamics of slender fibers immersed in an incompressible

    fluid. Specifically, we consider microscopic, rigid fibers, that

    sediment due to gravity. Such fibers make up the micro-structure of many

    suspensions for which the macroscopic dynamics are not well understood.

    Our numerical algorithm is based on a non-local slender body approximation

    that yields a system of coupled integral equations, relating the forces

    exerted on the fibers to their velocities, which takes into account the hydrodynamic

    interactions of the fluid and the fibers. The system is closed by

    imposing the constraints of rigid body motions.

    The fact that the fibers are straight have been further exploited in the

    design of the numerical method, expanding the force on Legendre polynomials

    to take advantage of the specific mathematical structure of a finite-part

    integral operator, as well as introducing analytical quadrature in a manner

    possible only for straight fibers.

    We have carefully treated issues of accuracy, and present convergence

    results for all numerical parameters before we finally discuss the results from

    simulations including a larger number of fibers.

  • 6.
    Gustavsson, Katarina
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Gravity induced sedimentation of slender fibers2009In: Physics of fluids, ISSN 1070-6631, E-ISSN 1089-7666, Vol. 21, no 12Article in journal (Refereed)
    Abstract [en]

    Gravity induced sedimentation of slender, rigid fibers in a highly viscous fluid is investigated by large scale numerical simulations. The fiber suspension is considered on a microscopic level and the flow is described by the Stokes equations in a three dimensional periodic domain. Numerical simulations are performed to study in great detail the complex dynamics of a cluster of fibers. A repeating cycle is identified. It consists of two main phases: a densification phase, where the cluster densifies and grows, and a coarsening phase, during which the cluster becomes smaller and less dense. The dynamics of these phases and their relation to fluctuations in the sedimentation velocity are analyzed. Data from the simulations are also used to investigate how average fiber orientations and sedimentation velocities are influenced by the microstructure in the suspension. The dynamical behavior of the fiber suspension is very sensitive to small random differences in the initial configuration and a number of realizations of each numerical experiment are performed. Ensemble averages of the sedimentation velocity and fiber orientation are presented for different values of the effective concentration of fibers and the results are compared to experimental data. The numerical code is parallelized using the Message Passing Instructions (MPI) library and numerical simulations with up 800 fibers can be run for very long times which is crucial to reach steady levels of the averaged quantities. The influence of the periodic boundary conditions on the process is also carefully investigated.

  • 7.
    Marin, Oana
    et al.
    KTH, School of Engineering Sciences (SCI).
    Gustavsson, Katarina
    KTH, School of Engineering Sciences (SCI).
    Tornberg, Anna-Karin
    KTH, School of Engineering Sciences (SCI).
    A fast summation method for fiber simulationsManuscript (preprint) (Other academic)
  • 8.
    Marin, Oana
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA (closed 2012-06-30). KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    A highly accurate boundary treatment for confined Stokes flow2012In: Computers & Fluids, ISSN 0045-7930, E-ISSN 1879-0747, Vol. 66, p. 215-230Article in journal (Refereed)
    Abstract [en]

    Fluid flow phenomena in the Stokesian regime abounds in nature as well as in microfluidic applications. Discretizations based on boundary integral formulations for such flow problems allow for a reduction in dimensionality but have to deal with dense matrices and the numerical evaluation of integrals with singular kernels. The focus of this paper is the discretization of wall confinements, and specifically the numerical treatment of flat solid boundaries (walls), for which a set of high-order quadrature rules that accurately integrate the singular kernel of the Stokes equations are developed. Discretizing by Nystrom's method, the accuracy of the numerical integration determines the accuracy of the solution of the boundary integral equations, and a higher order quadrature method yields a large gain in accuracy at negligible cost. The structure of the resulting submatrix associated with each wall is exploited in order to substantially reduce the memory usage. The expected convergence of the quadrature rules is validated through numerical tests, and this boundary treatment is further applied to the classical problem of a sedimenting sphere in the vicinity of solid walls.

  • 9.
    Marin, Oana
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Tornberg, Anna-Karin
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A wall treatment for confined Stokes flowArticle in journal (Other academic)
    Abstract [en]

     

    The study of bodies immersed in Stokes flow is crucial in various microfluidic applications. Recasting the governing equations in a boundary integral formulation reduces the three-dimensional problem to two-dimensional integral equations to be discretized over the surface of the submerged objects. The present work focuses on the development and validation of a wall treatment where the wall is discretized in the same fashion as the immersed bodies. For this purpose, a set of high-order quadrature rules for the numerical integration of integrals containing the singular Green’s function-the so-called Stokeslet - has been developed. By coupling the wall discretization to the discretization of immersed objects, we exploit the structure of the block matrix corresponding to the wall discretization in order to substantially reduce the memory usage. For validation, the classical problem of a sedimenting sphere in the vicinity of solid walls is studied.

  • 10.
    Sjögreen, Björn
    et al.
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Gustavsson, Katarina
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    Gudmundsson, Reynir Levi
    KTH, Superseded Departments, Numerical Analysis and Computer Science, NADA.
    A model for peak formation in the two-phase equations2004Report (Other academic)
  • 11.
    Sjögreen, Björn
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gudmundsson, Reynir Levi
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A model for peak formation in the two-phase equations2007In: Mathematics of Computation, ISSN 0025-5718, E-ISSN 1088-6842, Vol. 76, no 260, p. 1925-1940Article in journal (Refereed)
    Abstract [en]

    We present a hyperbolic-elliptic model problem related to the equations of two-phase fluid flow. The model problem is solved numerically, and properties of its solution are presented. The model equation is well-posed when linearized around a constant state, but there is a strong focusing effect, and very large solutions exist at certain times. We prove that the model problem has a smooth solution for bounded times.

  • 12.
    Tornberg, Anna-Karin
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis and Computer Science, NADA.
    A numerical method for simulations of rigid fiber suspensions2006In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 215, no 1, p. 172-196Article in journal (Refereed)
    Abstract [en]

    In this paper, we present a numerical method designed to simulate the challenging problem of the dynamics of slender fibers immersed in an incompressible fluid. Specifically, we consider microscopic, rigid fibers, that sediment due to gravity. Such fibers make up the micro-structure of many suspensions for which the macroscopic dynamics are not well understood. Our numerical algorithm is based on a non-local slender body approximation that yields a system of coupled integral equations, relating the forces exerted on the fibers to their velocities, which takes into account the hydrodynamic interactions of the fluid and the fibers. The system is closed by imposing the constraints of rigid body motions. The fact that the fibers are straight have been further exploited in the design of the numerical method, expanding the force on Legendre polynomials to take advantage of the specific mathematical structure of a finite-part integral operator, as well as introducing analytical quadrature in a manner possible only for straight fibers. We have carefully treated issues of accuracy, and present convergence results for all numerical parameters before we finally discuss the results from simulations including a larger number of fibers.

  • 13.
    Zahedi, Sara
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Kreiss, Gunilla
    Division of Scientific Computing, Department of Information Technology, Uppsala University.
    A Conservative Level Set Method for Contact Line Dynamics2009In: Journal of Computational Physics, ISSN 0021-9991, E-ISSN 1090-2716, Vol. 228, no 17, p. 6361-6375Article in journal (Refereed)
    Abstract [en]

    A new model for simulating contact line dynamics is proposed. We apply the idea of driving contact-line movement by enforcing the equilibrium contact angle at the boundary, to the conservative level set method for incompressible two-phase flow [E. Olsson, G. Kreiss, A conservative level set method for two phase flow, J. Comput. Phys. 210 (2005) 225-246]. A modified reinitialization procedure provides a diffusive mechanism for contact-line movement, and results in a smooth transition of the interface near the contact line without explicit reconstruction of the interface. We are able to capture contact-line movement without loosing the conservation. Numerical simulations of capillary dominated flows in two space dimensions demonstrate that the model is able to capture contact line dynamics qualitatively correct.

  • 14.
    Zahedi, Sara
    et al.
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    Kreiss, Gunilla
    Gustavsson, Katarina
    KTH, School of Computer Science and Communication (CSC), Numerical Analysis, NA.
    An Interface Capturing Method for Two-Phase Flow with Moving Contact Lines2008In: Proccedings of the 1st European Conference on Microfluidics 2008, SOCIETE HYDROTECHNIQUE DE FRANCE , 2008Conference paper (Refereed)
  • 15.
    Zhang, Feng
    et al.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Dahlkild, Anders A.
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Gustavsson, Katarina
    KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Numerical Analysis, NA. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW.
    Lundell, Fredrik
    KTH, School of Engineering Sciences (SCI), Mechanics. KTH, School of Engineering Sciences (SCI), Centres, Linné Flow Center, FLOW. KTH, School of Chemical Science and Engineering (CHE), Centres, Wallenberg Wood Science Center.
    Near-Wall Convection in a Sedimenting Suspension of Fibers2014In: AIChE Journal, ISSN 0001-1541, E-ISSN 1547-5905, Vol. 60, no 12, p. 4253-4265Article in journal (Refereed)
    Abstract [en]

    The sedimentation of a fiber suspension near a vertical wall is investigated numerically. Initially, the near-wall convection is an upward backflow, which originates from the combined effects of the steric-depleted layer and a hydrodynamically depleted region near the wall. The formation of the hydrodynamically depleted region is elucidated by a convection-diffusion investigation, in which fibers are classified according to the different directions in which they drift. For fibers with sufficiently large aspect ratio, the initial near-wall backflow keeps growing. However, the backflow reverses to downward flow at later times if the aspect ratio is small. This is due to the fiber-wall interactions which rotate fibers to such angles that make fibers drift away from the wall, inducing a dense region and a correspondingly downward flow outside the initial backflow. Moreover, the steric-depleted boundary condition is of secondary importance in the generation and evolution of the near-wall convection.

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