Browsing by Author "Hu, Wei-Fan"

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A coupled immersed boundary and immersed interface method for interfacial flows with soluble surfactant
(2018-05-30)
Hu, Wei-Fan
;
Lai, Ming-Chih
;
Misbah, Chaouqi
;
應用數學系
;
Department of Applied Mathematics
In this paper, we develop a coupled immersed boundary (IB) and immersed interface method (IIM) to simulate the interfacial flow problems with soluble surfactant. That is, a coupled system of surface-bulk convection-diffusion equations must be solved not only on a moving interface but also in an evolving irregular domain. Based on the immersed interface framework, we first begin with the numerical development for the diffusion equation in a fixed irregular domain and then extend the scheme to solve the convection-diffusion equation in an evolving domain. The fluid motion governed by the incompressible Navier-Stokes equations is solved by using traditional immersed boundary method while the bulk surfactant is solved by the proposed immersed interface method. A series of numerical tests for the present scheme have been conducted to illustrate the accuracy and applicability of the method. We first perform the accuracy and efficiency tests for the present IIM solver. We then check the convergence of the surface and bulk surfactant and the fluid variables in the interfacial flow problems. We further run a series of numerical simulations for a suspended droplet under shear flow with presence of soluble surfactant to study the effects of the dimensionless Biot number and the bulk Peclet number on the droplet deformation in details. (C) 2018 Elsevier Ltd. All rights reserved.
A coupled immersed interface and grid based particle method for three-dimensional electrohydrodynamic simulations
(2019-12-01)
Hsu, Shih-Hsuan
;
Hu, Wei-Fan
;
Lai, Ming-Chih
;
應用數學系
;
Department of Applied Mathematics
In the present work, we propose a coupled immersed interface and grid based particle method to solve two-phase electrohydrodynamic problems in three dimensions. The problem considers a leaky dielectric (weakly conducting) droplet immersed in another leaky dielectric fluid under electric field where the non-homogeneous droplet surface charge effect is taken into account. Due to the mismatch of electrical properties between two fluids, the electric potential satisfying Laplace equation with jump conditions across the droplet surface is coupled with the conservation equation for the surface charge density. Consequently, we first develop a three-dimensional augmented immersed interface method (IIM) which incorporates some known jump conditions naturally along the normal direction and check the desired accuracy. Here, the grid based particle method (GBPM) is used to track the interface by the projection of the neighboring Eulerian grid points so no requirement for stitching of parameterizations nor body fitted moving meshes. Within the leaky dielectric framework, the electric stress can be treated as an interfacial force so that both the surface tension and electric force can be formulated in a unified continuum force in the Navier-Stokes equations. A series of numerical tests have been carefully conducted to illustrate the accuracy and applicability of the present method to simulate droplet electrohydrodynamics. In particular, we investigate the droplet equilibrium dynamics under weak and strong electric fields in detail. It is interesting to find out a chaotic tumbling motion with irregular rotating modes which we believe that is the first numerical verification to the recent experiments. (C) 2019 Elsevier Inc. All rights reserved.
A direct Poisson solver in spherical geometry with an application to diffusiophoretic problems
(2020-05-15)
Lin, Te-Sheng
;
Hu, Wei-Fan
;
Misbah, Chaouqi
;
應用數學系
;
Department of Applied Mathematics
We propose a simple and efficient class of direct solvers for Poisson equation in finite or infinite domains related to spherical geometry. The solver was developed based on truncated spherical harmonics expansion, where the differential mode equations were solved by second-order finite difference method without handling coordinate singularities. The solver was further extended to study the dynamics of a diffusiophoretic particle suspended in Stokes flow. Numerical experiments suggested that the particle can achieve a self-sustained unidirectional motion at moderate Peclet numbers, whereas the particle motion becomes chaotic in high Peclet number regimes. The statistical analysis illustrates the run-and-tumble-like nature at short times and diffusive nature at long times without any source of noise. (C) 2020 Elsevier Inc. All rights reserved.
A FRACTIONAL STEP IMMERSED BOUNDARY METHOD FOR STOKES FLOW WITH AN INEXTENSIBLE INTERFACE ENCLOSING A SOLID PARTICLE
(2012)
Lai, Ming-Chih
;
Hu, Wei-Fan
;
Lin, Wen-Wei
;
應用數學系
;
數學建模與科學計算所(含中心)
In this paper, we develop a fractional step method based on the immersed boundary (IB) formulation for Stokes flow with an inextensible (incompressible) interface enclosing a solid particle. In addition to solving for the fluid variables such as the velocity and pressure, the present problem involves finding an extra unknown elastic tension such that the surface divergence of the velocity is zero along the interface, and an extra unknown particle surface force such that the velocity satisfies the no-slip boundary condition along the particle surface. While the interface moves with local fluid velocity, the enclosed particle hereby undergoes a rigid body motion, and the system is closed by the force-free and torque-free conditions along the particle surface. The equations are then discretized by standard centered difference schemes on a staggered grid, and the interactions between the interface and particle with the fluid are discretized using a discrete delta function as in the IB method. The resultant linear system of equations is symmetric and can be solved by fractional steps so that only fast Poisson solvers are involved. The present method can be extended to Navier-Stokes flow with moderate Reynolds number by treating the nonlinear advection terms explicitly for the time integration. The convergent tests for a Stokes solver with or without an inextensible interface are performed and confirm the desired accuracy. The tank-treading to tumbling motion for an inextensible interface enclosing a solid particle with different filling fractions under a simple shear flow has been studied extensively, and the results here are in good agreement with those obtained in literature.
A hybrid immersed boundary and immersed interface method for electrohydrodynamic simulations
(2015-02-01)
Hu, Wei-Fan
;
Lai, Ming-Chih
;
Young, Yuan-Nan
;
應用數學系
;
數學建模與科學計算所(含中心)
In this paper, we develop a hybrid immersed boundary (IB) and immersed interface method (IIM) to simulate the dynamics of a drop under an electric field in Navier-Stokes flows. Within the leaky dielectric framework with piecewise constant electric properties in each fluid, the electric stress can be treated as an interfacial force on the drop interface. Thus, both the electric and capillary forces can be formulated in a unified immersed boundary framework. The electric potential satisfies a Laplace equation which is solved numerically by an augmented immersed interface method which incorporates the jump conditions naturally along the normal direction. The incompressible Navier-Stokes equations for the fluids are solved using a projection method on a staggered MAC grid and the potential is solved at the cell center. The interface is tracked in a Lagrangian manner with mesh control by adding an artificial tangential velocity to transport the Lagrangian markers to ensure that the spacing between markers is uniform throughout the computations. A series of numerical tests for the present scheme have been conducted to illustrate the accuracy and applicability of the method. We first compute the potential and its gradient (electric field) to perform the accuracy check for the present augmented IIM. We then check the convergence of the interfacial electric force and the fluid variables. We further run a series of simulations with different permittivity and conductivity ratios and compare with the results obtained by the small deformation theory and other numerical results in literature. In addition, we also study the electric effect for a drop under shear flow. (C) 2014 Elsevier Inc. All rights reserved.
Amoeboid swimming in a channel
(2016)
Wu, Hao
;
Farutin, Alexander
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Hu, Wei-Fan
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Thiebaud, Marine
;
Rafai, Salima
Several micro-organisms, such as bacteria, algae, or spermatozoa, use flagellar or ciliary activity to swim in a fluid, while many other micro-organisms instead use ample shape deformation, described as amoeboid, to propel themselves either by crawling on a substrate or swimming. Many eukaryotic cells were believed to require an underlying substratum to migrate (crawl) by using membrane deformation (like blebbing or generation of lamellipodia) but there is now increasing evidence that a large variety of cells (including those of the immune system) can migrate without the assistance of focal adhesion, allowing them to swim as efficiently as they can crawl. This paper details the analysis of amoeboid swimming in a confined fluid by modeling the swimmer as an inextensible membrane deploying local active forces (with zero total force and torque). The swimmer displays a rich behavior: it may settle into a straight trajectory in the channel or navigate from one wall to the other depending on its confinement. The nature of the swimmer is also found to be affected by confinement: the swimmer can behave, on average over one swimming cycle, as a pusher at low confinement, and becomes a puller at higher confinement, or vice versa. The swimmer\'s nature is thus not an intrinsic property. The scaling of the swimmer velocity V with the force amplitude A is analyzed in detail showing that at small enough A, V similar to A(2)/eta(2) (where eta is the viscosity of the ambient fluid), whereas at large enough A, V is independent of the force and is determined solely by the stroke cycle frequency and the swimmer size. This finding starkly contrasts with models where motion is based on ciliary and flagellar activity, where V similar to A/eta. To conclude, two definitions of efficiency as put forward in the literature are analyzed with distinct outcomes. We find that one type of efficiency has an optimum as a function of confinement while the other does not. Future perspectives are outlined.
An immersed boundary method for simulating the dynamics of three-dimensional axisymmetric vesicles in Navier-Stokes flows
(2014-01-15)
Hu, Wei-Fan
;
Kim, Yongsam
;
Lai, Ming-Chih
;
應用數學系
;
數學建模與科學計算所(含中心)
In this paper, we develop a simple immersed boundary method to simulate the dynamics of three-dimensional axisymmetric inextensible vesicles in Navier-Stokes flows. Instead of introducing a Lagrange's multiplier to enforce the vesicle inextensibility constraint, we modify the model by adopting a spring-like tension to make the vesicle boundary nearly inextensible so that solving for the unknown tension can be avoided. We also derive a new elastic force from the modified vesicle energy and obtain exactly the same form as the originally unmodified one. In order to represent the vesicle boundary, we use Fourier spectral approximation so we can compute the geometrical quantities on the interface more accurately. A series of numerical tests on the present scheme have been conducted to illustrate the applicability and reliability of the method. We first perform the accuracy check of the geometrical quantities of the interface, and the convergence check for different stiffness numbers as well as fluid variables. Then we study the vesicle dynamics in quiescent flow and in gravity. Finally, the shapes of vesicles in Poiseuille flow are investigated in detail to study the effects of the reduced volume, the confinement, and the mean flow velocity. The numerical results are shown to be in good agreement with those obtained in literature. (C) 2013 Elsevier Inc. All rights reserved.
An immersed boundary method for simulating vesicle dynamics in three dimensions
(2016-10-01)
Seol, Yunchang
;
Hu, Wei-Fan
;
Kim, Yongsam
;
Lai, Ming-Chih
;
應用數學系
We extend our previous immersed boundary (IB) method for 3D axisymmetric inextensible vesicle in Navier-Stokes flows (Hu et al., 2014 [17]) to general three dimensions. Despite a similar spirit in numerical algorithms to the axisymmetric case, the fully 3D numerical implementation is much more complicated and is far from straightforward. A vesicle membrane surface is known to be incompressible and exhibits bending resistance. As in 3D axisymmetric case, instead of keeping the vesicle locally incompressible, we adopt a modified elastic tension energy to make the vesicle surface patch nearly incompressible so that solving the unknown tension (Lagrange multiplier for the incompressible constraint) can be avoided. Nevertheless, the new elastic force derived from the modified tension energy has exactly the same mathematical form as the original one except the different definitions of tension. The vesicle surface is discretized on a triangular mesh where the elastic tension and bending force are calculated on each vertex (Lagrangian marker in the IB method) of the triangulation. A series of numerical tests on the present scheme are conducted to illustrate the robustness and applicability of the method. We perform the convergence study for the immersed boundary forces and the fluid velocity field. We then study the vesicle dynamics in various flows such as quiescent, simple shear, and gravitational flows. Our numerical results show good agreements with those obtained in previous theoretical, experimental and numerical studies. (C) 2016 Elsevier Inc. All rights reserved.
An Unconditionally Energy Stable Immersed Boundary Method with Application to Vesicle Dynamics
(2013-08-01)
Hu, Wei-Fan
;
Lai, Ming-Chih
;
應用數學系
;
數學建模與科學計算所(含中心)
;
Department of Applied Mathematics
We develop an unconditionally energy stable immersed boundary method, and apply it to simulate 2D vesicle dynamics. We adopt a semi-implicit boundary forcing approach, where the stretching factor used in the forcing term can be computed from the derived evolutional equation. By using the projection method to solve the fluid equations, the pressure is decoupled and we have a symmetric positive definite system that can be solved efficiently. The method can be shown to be unconditionally stable, in the sense that the total energy is decreasing. A resulting modification benefits from this improved numerical stability as the time step size can be significantly increased (the severe time step restriction in an explicit boundary forcing scheme is avoided). As an application, we use our scheme to simulate vesicle dynamics in Navier-Stokes flow.
Chaotic Swimming of Phoretic Particles
(2019-12-03)
Hu, Wei-Fan
;
Lin, Te-Sheng
;
Rafai, Salima
;
Misbah, Chaouqi
;
應用數學系
The swimming of a rigid phoretic particle in an isotropic fluid is studied numerically as a function of the dimensionless solute emission rate (or Peclet number Pe). The particle sets into motion at a critical Pe. Whereas the particle trajectory is straight at a small enough Pe, it is found that it loses its stability at a critical Pe in favor of a meandering motion. When Pe is increased further, the particle meanders at a short scale but its trajectory wraps into a circle at a larger scale. Increasing even further, Pe causes the swimmer to escape momentarily the circular trajectory in favor of chaotic motion, which lasts for a certain time, before regaining a circular trajectory, and so on. The chaotic bursts become more and more frequent as Pe increases, until the trajectory becomes fully chaotic, via the intermittency scenario. The statistics of the trajectory is found to be of the run-and-tumble-like nature at a short enough time and of diffusive nature at a long time without any source of noise.
Vesicle electrohydrodynamic simulations by coupling immersed boundary and immersed interface method
(2016-07-15)
Hu, Wei-Fan
;
Lai, Ming-Chih
;
Seol, Yunchang
;
Young, Yuan-Nan
;
應用數學系
In this paper, we develop a coupled immersed boundary (IB) and immersed interface method (IIM) to simulate the electrodeformation and electrohydrodynamics of a vesicle in Navier-Stokes leaky dielectric fluids under a DC electric field. The vesicle membrane is modeled as an inextensible elastic interface with an electric capacitance and an electric conductance. Within the leaky dielectric framework and the piecewise constant electric properties in each fluid, the electric stress can be treated as an interfacial force so that both the membrane electric and mechanical forces can be formulated in a unified immersed boundary method. The electric potential and transmembrane potential are solved simultaneously via an efficient immersed interface method. The fluid variables in Navier-Stokes equations are solved using a projection method on a staggered MAC grid while the electric potential is solved at the cell center. A series of numerical tests have been carefully conducted to illustrate the accuracy and applicability of the present method to simulate vesicle electrohydrodynamics. In particular, we investigate the prolateoblate-prolate (POP) transition and the effect of electric field and shear flow on vesicle electrohydrodynamics. Our numerical results are in good agreement with those obtained in previous work using different numerical algorithms. (C) 2016 Elsevier Inc. All rights reserved.