H.S. Udaykumar

ELAFINT :a mixed Eulerian-Lagrangian method for fluid flows with complex and moving boundaries

In this work a mixed Eulerian–Lagrangian technique is devised, hereinafter abbreviated as ELAFINT (Eulerian–Lagrangian Algorithm For INterface Tracking). The method is capable of handling fluid flows in the presence of both irregularly shaped solid boundaries and moving/free phase boundaries. The position and shape of the boundary are tracked explicitly by the Lagrangian translation of marker particles. The field equations are solved on an underlying fixed grid as in Eulerian methods. The interface passes through the grid lay-out and details regarding the treatment of the cut cells so formed are provided. The issues involved in treating the internal boundaries are dealt with, with particular attention to conservation and consistency in the vicinity of the interface. The method is tested by comparing with solutions from well-tested body-fitted co-ordinate methods. Test cases pertaining to forced and natural convection in irregular geometries and moving phase boundaries with melt convection are presented. The capability developed here can be beneficial in solving difficult flow problems involving moving and geometrically complex boundaries.

Hydrodynamics of a compound drop with application to leukocyte modeling

We study the dynamics of a compound liquid drop which is comprised of an outer membrane surface, a shell layer, and a core. The deformation due to an imposed extensional flow and the subsequent recovery are investigated computationally employing a combined Eulerian–Lagrangian technique. The numerical method allows for large viscosity and capillarity differences between layers. The present study reports several findings which provide direct insight into developing a dynamic model for leukocytes. A compound drop behaves like a homogeneous, simple liquid drop if the core is sufficiently deformed and the time scale of the core, related to the combination of its viscosity and capillarity, is comparable to that of the shell layer. Disparate time scales between the core and shell layer result in a rapid initial recoil of the drop during which the shell fluid is the primary participant in the hydrodynamics, followed by a slower relaxation period during which the core and shell layer interact with each other. Cons...

Effects of Nucleus on Leukocyte Recovery

AbstractThe rheological properties of a leukocyte significantly affect its biological and mechanical characteristics. To date, existing physical models of leukocyte are not capable of quantitatively explaining the wide range of deformation and recovery behaviors observed in experiment. However, a compound drop model has gained some success. In the present work, we investigate the effect of nucleus size and position, and the relative rheological properties of cytoplasm and nucleus, on cell recovery dynamics. Two nucleus sizes corresponding to that of neutrophil and lymphocyte are considered. Direct comparison between numerical simulations and experimental observation is made. Results indicate that the time scale ratio between the nucleus and cytoplasm plays an important role in cell recovery characteristics. Comparable time scales between the two cell components yield favorable agreement in recovery rates between numerical and experimental observations; disparate time scales, on the other hand, result in recovery behavior and cell shapes inconsistent with experiments. Furthermore, it is found that the nucleus eccentricity exhibits minimum influence on all major aspects of the cell recovery characteristics. The present work offers additional evidence in support of the compound cell model for predicting the rheological behavior of leukocytes.

Rheological modelling of leukocytes

A three-layer Newtonian model is investigated using a combined Eulerian-Lagrangian computational method to describe the dynamic behaviour of leukocytes. The model, composed of a cell membrane (outer layer), cytoplasm (middle layer) and nucleus (inner layer), can better describe the recovery characteristics because large viscosity and capillarity differences between layers are considered, and both Newtonian and seemingly non-Newtonian behaviours reported in the literature can be reproduced. It is found that, to describe adequately the various rheological characteristics of leukocytes, the presence of the highly viscous nucleus and its deformation/recovery, as well as the surface energy stored in the fluid interfaces, are critical. Photographs from pipette experiments using a fluorescent technique confirm the theoretical finding of the important role played by the nucleus in cell deformation.

On the suppression of numerical oscillations using a non-linear filter

The idea of using a non-linear filtering algorithm to eliminate numerically generated oscillations is investigated. A detailed study is conducted to follow the development of numerical oscillations and their interaction with the filter. A relaxation procedure is also proposed to enhance the effectiveness of the filter. Three model problems, a 2D steady state scalar convection-diffusion equation, a 1D unsteady gas dynamics flow with shock and a 1D linear wave equation, have been designed to test the performance of the filtering algorithm. The effectiveness of the filter is assessed for convection schemes of different dispersive and diffusive characteristics, demonstrating that it is effective in eliminating oscillations with short wavelength, but oscillations of longer wavelengths are virtually unaffected. It is concluded that a proper combination of non-linear filter and dispersive numerical scheme is a viable alternative to dissipative schemes in resolving flows with sharp gradients and discontinuities.

A GRID-SUPPORTED MARKER PARTICLE SCHEME FOR INTERFACE TRACKING

Abstract A methodology is presented to simulate the growth and interaction of unstable fronts. Such fronts are found to be important in instabilities arising in several natural and industrial processes, such as solidification, spray dynamics, and bubble growth. The numerical simulation of such phenomena is challenging on account of the highly distorted moping boundary at which, often, curvature-dependent boundary conditions need be applied in each phase. Herein is presented a numerical technique to capture highly distorted interfaces. The interface is represented employing marker particles. Joining successive markers with circular arcs yields values of curvatures and normals on the interface. The markers are followed over an underlying Cartesian grid and new marker particles are generated at each time step by an intersection procedure. The issue of mergers of interfaces is also attacked and the use of cells permits the simulation of merger-breakup processes. Thus, the method presented here, unlike previou...

Simulation of interfacial instabilities during solidification—I. Conduction and capillarity effects

Abstract A combined Eulerian-Lagrangian numerical method is developed for simulating deformed interfaces arising in the solidification of pure materials. The interface tracking procedure employs marker particles and is the Lagrangian component of the calculation. The field equations are solved in a fixed Eulerian framework, so that the interface passes through the grid layout. Information from the explicitly tracked interface is used to apply boundary conditions at the exact interface location in each computational cell, in contrast with other Eulerian schemes. Consistent with the the established theory, in the absence of surface tension, the present simulations result in different types of behavior such as tip-splitting and cusp formation. For low surface tensions, due to the lack of physical length scales, the solutions are qualitatively affected by grid resolution with no unique solution available. In contrast, with substantial surface tension values the initial perturbation grows to form long fingers. The finger shapes reflect the stabilizing effects of capillarity. Unique solutions can be reached with nonzero surface tension.

An interface tracking method applied to morphological evolution during phase change

Abstract The focus of this work is the numerical simulation of interface motion during solidification of pure materials. First, we assess the applicability of the oft-used quasi-stationary approximation for interface motion. Such an approximation results in poor accuracy for non-trivial Stefan numbers. Next, a generic interface tracking procedure is designed, which overcomes restrictions of single-valuedness of the interface imposed by commonly used mapping methods. This method incorporates with ease interface phenomena involving curvature, which assume importance at the smaller scales of a deformed interface. The method is then applied to study the development of a morphologically unstable phase interface. The issue of appropriate scaling has been addressed. The Gibbs-Thomson effect for curved interfaces has been included. The evolution of the interface, with the competing mechanisms of undercooling and surface tension is found to culminate in tip-splitting, cusp formation and persistent cellular development.

Numerical Analysis of the Deformation of an Adherent Drop Under Shear Flow

The adhesion of leukocytes to substrates is an important biomedical problem and has drawn extensive research. In this study, employing both single and compound drop models, we investigate how hydrodynamics interacts with an adherent liquid drop in a shear flow. These liquid drop models have recently been used to describe the rheological behavior of leukocytes. Numerical simulation confirms that the drop becomes more elongated when either capillary number or initial contact angle increases. Our results show that there exists a thin region between the drop and the wall as the drop undergoes large stretching, which allows high pressure to build up and provides a lift force. In the literature, existing models regard the leukocyte as a rigid body to calculate the force and torque acting on the drop in order to characterize the binding between cell receptors and endothelial ligands. The present study indicates that such a rigid body model is inadequate and the force magnitude obtained from it is less than half of that obtained using the deformable drop models. Furthermore, because of its much higher viscosity, the cell nucleus introduces a hydrodynamic time scale orders of magnitude slower than the cytoplasm. Hence the single and compound drops experience different dynamics during stretching, but exhibit very comparable steady-state shapes. The present work offers a framework to facilitate the development of a comprehensive dynamic model for blood cells.

Structured moving grid and geometric conservation laws for fluid flow computation

Fluid flow analysis using structured moving boundary fitted grids is presented. This type of method can be applied to certain moving boundary problems. The Cartesian velocity components are made the primary variables, and grid motion and geometric conservation are handled in a natural way through the contravariant velocities and the Jacobian evaluations. A SIMPLE-based sequential solver along with a staggered grid is employed. Furthermore, appropriate treatments of the discretized form of the diffusion term on a nonorthogonal skewed grid are also discussed. The moving grid approach is applied to simulate test problems involving phase change.