# Sashikumaar GanesanIndian Institute of Science | IISC · Department of Computational and Data Sciences

Sashikumaar Ganesan

Dr.rer.nat (PhD)

## About

52

Publications

9,409

Reads

**How we measure 'reads'**

A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more

1,339

Citations

Introduction

## Publications

Publications (52)

Stability and error estimate for the Oseen equations in a projection based variational setup has been derived in this paper. The use of Geometric Conservation Law (GCL) provides unconditional stability whereas without using GCL we have a conditional scheme which imposes restriction on the time step. Further using the stability results derived, we m...

We study two-phase and free surface flows with soluble and insoluble surfactants. A numerical analysis of the contained convection-diffusion equations is carried out. The surface equation is stabilized by Local Projection Stabilization. The benefit of Local Projection Stabilization on surfaces is shown by a numerical example. An advanced finite ele...

ParMooN is a program package for the numerical solution of elliptic and parabolic partial differential equations. It inherits the distinct features of its predecessor MooNMD (John and Matthies, 2004): strict decoupling of geometry and finite element spaces, implementation of mapped finite elements as their definition can be found in textbooks, and...

A finite element scheme for the solution of a cancer invasion model is proposed. The cancer dynamics model consists of three coupled partial differential equations which describe the evolution of cancer cell density, extra cellular matrix and the matrix degrading enzymes. The model incorporates proliferation and haptotaxis effect of cancer cells, t...

http://www.cambridgeindia.org/books/searchedbook/Finite-Elements/9781108415705
Finite element method (FEM) is a numerical technique for approximation of the solution of partial differential equations. This book on FEM and related simulation tools starts with a brief introduction to Sobolev spaces and elliptic scalar problems and continues with exp...

A temperature-dependent dynamic contact angle as a function of temperature-dependent surface tension and reference equilibrium contact angle is proposed for modeling of moving contact line flows, in particular, for computations of liquid droplet impingement on a hot solid substrate. The fluid flow in the liquid droplet is described by the time-depe...

A variational multiscale method for computations of incompressible Navier–Stokes equations in time-dependent domains is presented. The proposed scheme is a three-scale variational multiscale method with a projection based scale separation that uses an additional tensor valued space for the large scales. The resolved large and small scales are compu...

Three-dimensional finite element computations of a cancer invasion model with nonlinear density-dependent diffusion and haptotactic sensitivity function are presented. The nonlinear model includes three key variables, namely the cancer cell density, the extra cellular matrix (ECM) density and the matrix degrading enzymes (MDE) concentration. In ord...

Modeling of continuous and controlled nanocrystal synthesis in a microfluidic reactor is presented. The population balance model that describes the nanocrystal synthesis consists of a population balance equation and a set of species concentration equations. In order to incorporate the effects of both reaction and diffusion limited growth conditions...

Parallel finite element algorithms based on object-oriented concepts are presented. Moreover, the design and implementation of a data structure proposed are utilized in realizing a parallel geometric multigrid method. The ParFEMapper and the ParFECommunicator are the key components of the data structure in the proposed parallel scheme. These classe...

In this paper we propose a non-conforming exponentially accurate least-squares spectral element method for Oseen equations in primitive variable formulation which is applicable to both two and three dimensional domains. First order reformulation is avoided and the condition number is controlled by a suitable preconditioner for velocity components a...

Stability estimates for Streamline Upwind Petrov-Galerkin (SUPG) finite element method with different time integration schemes for the solution of a scalar transient convection-diffusion-reaction equation in a time-dependent domain are derived. The deformation of the domain is handled with the arbitrary Lagrangian-Eulerian (ALE) approach. In partic...

Numerical simulation of turbulent flows over different aerofoil configurations are presented in this paper. The incompressible fluid flow is described by the time-dependent incompressible Navier–Stokes equations. Further, a finite element variational multiscale method is used to simulate the turbulent flows. Computation over a cylinder and differen...

An arbitrary Lagrangian--Eulerian (ALE) finite element scheme for
computations of soluble surfactant droplet impingement on a horizontal surface
is presented. The numerical scheme solves the time-dependent Navier--Stokes
equations for the fluid flow, scalar convection-diffusion equation for the
surfactant transport in the bulk phase, and simultaneo...

The Streamline Upwind Petrov--Galerkin (SUPG) finite element method for a
transient convection-diffusion-reaction equation in time-dependent domains is
proposed and studied. In particular, a stabilized numerical scheme for a
convection dominated transient scalar problem in deforming domains is
developed. The time-dependent domain is handle by the a...

An operator-splitting finite element method for solving high-dimensional parabolic equations is presented. The stability and the error estimates are derived for the proposed numerical scheme. Furthermore, two variants of fully-practical operator-splitting finite element algorithms based on the quadrature points and the nodal points, respectively, a...

The terahertz propagation in real tissues causes heating as with any other electromagnetic radiation propagation. A finite element model that provides numerical solutions to the heat conduction equation coupled with realistic models of tissues is employed in this work to compute the temperature raise due to terahertz propagation. The results indica...

We present a heterogeneous finite element method for the solution of a high-dimensional population balance equation, which depends both the physical and the internal property coordinates. The proposed scheme tackles the two main difficulties in the finite element solution of population balance equation: (i) spatial discretization with the standard...

Effects of dynamic contact angle models on the flow dynamics of an impinging droplet in sharp interface simulations are presented in this article. In the considered finite element scheme, the free surface is tracked using the arbitrary Lagrangian–Eulerian approach. The contact angle is incorporated into the model by replacing the curvature with the...

A finite element method for solving multidimensional population balance systems is proposed where the balance of fluid velocity, temperature and solute partial density is considered as a two-dimensional system and the balance of particle size distribution as a three-dimensional one. The method is based on a dimensional splitting into physical space...

Numerical computations of two-phase flows with surface active agents (surfactants) are highly demanded in several scientific and engineering applications. Apart from the other challenges associated with the computation of two-phase flows, the presence of surfactants increases the complexity. Surfactants alter the flow dynamics significantly by lowe...

Crystallization processes are characterized by close interaction between particle formation and fluid flow. A detailed physical description of these processes leads to complicated high-order models whose numerical solution is challenging and computationally expensive. For advanced process control and other model based real-time applications, reduce...

Oscillations of droplets or bubbles of a confined fluid in a fluid environment are found in various situations in everyday life, in technological processing and in natural phenomena on different length scales. Air bubbles in liquids or liquid droplets in air are well-known examples. Soap bubbles represent a particularly simple, beautiful and attrac...

We give a survey on recent developments of stabilization methods based on local projection type. The considered class of problems
covers scalar convection–diffusion equations, the Stokes problem and the linearized Navier–Stokes equations. A new link of
local projection to the streamline diffusion method is shown. Numerical tests for different type...

This paper presents a numerical scheme for computing moving contact line flows with wetting effects. The numerical scheme
is based on Arbitrary Lagrangian Eulerian (ALE) finite elements on moving meshes. In the computations, the wetting effects
are taken into account through a weak enforcement of the prescribed equilibrium contact angle into the mo...

Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark quantities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence toward a reference solution. Comprehen...

A finite element scheme to compute the dynamics of insoluble surfactant on a deforming free surface is presented. The free surface is tracked by the arbitrary Lagrangian–Eulerian (ALE) approach, whereas the surfactant concentration transport equation is approximated in a Lagrangian manner. Since boundary resolved moving meshes are used in the ALE a...

The local projection stabilization allows us to circumvent the Babuska-Brezzi condition and to use equal order interpolation for discretizing the Stokes problem. The projection is usually done in a two-level approach by projecting the pressure gradient onto a discontinuous finite element space living on a patch of elements. We propose a new local p...

An accurate finite element scheme for computing 3D-axisymmetric incompressible free surface and interface flows is proposed. It is based on the arbitrary Lagrangian Eulerian (ALE) approach using free surface/interface-resolved moving meshes. Key features like the surface force, consisting of surface tension and the local curvature, and jumps in the...

A second-order finite element method for non-stationary Navier-Stokes equations with free capillary surface is proposed and applied to simulate the flow dynamics of a droplet after impinging on a solid surface.

Numerical investigations of the deformation of a single droplet are useful for better understanding of the macro behaviour of spray cooling. In this chapter we present a finite element scheme, which is developed for computations of a single liquid droplet deformation on a horizontal surface. The numerical scheme is based on an Arbitrary Lagrangian...

We show that a non-physical velocity may appear in the finite element calculation of incompressible two-phase flows subjected to an external local force. There are different sources responsible for this phenomenon: approximation of the incompressibility constraint, the interface, and the local external force. Furthermore, we demonstrate that this n...

Benchmark configurations for quantitative validation and comparison of incompressible interfacial flow codes, which model two-dimensional bubbles rising in liquid columns, are proposed. The benchmark quan-tities: circularity, center of mass, and mean rise velocity are defined and measured to monitor convergence towards a reference solution. Initial...

This work is devoted to the accurate simulation of incompressible two phase flows. The core of our methodology is the use of interface resolving meshes and the arbitrary Lagrangian-Eulerian (ALE) description of the fluid kinematics. Our numerical scheme is based on second order finite elements, a fractional step θ time discretisation, and a special...

This paper presents a technique to improve the velocity error in finite element solu- tions of the steady state Navier-Stokes equations. This technique is called pressure sep- aration. It relies upon subtracting the gradient of an appropriate approximation of the pressure on both sides of the Navier-Stokes equations. With this, the finite element e...

This paper presents the shape deformation of a single two dimensional spherical liquid droplet on a horizontal surface. The mathematical model can be defined by the time-dependent Navier-Stokes equations in a time-dependent domain. The model has to be completed by the free boundary condition on the fluid-gas interface and the Navier-slip boundary c...

A mathematical model for an non-isothermal liquid droplet deformation with dynamic contact angles on a horizontal solid surface is presented. The main challenges such as the inclusion of the contact angle in the model, prescribing the boundary condition at the moving contact line, Marangoni convection are addressed in our model. The solution is app...

The influence of continuous and discontinuous pressure appr oximation on spurious velocities is studied. The spurious velocities may generate in two-phase flows due to approximat ion errors in the curvature, in the incompressibility const raint, and in the pressure, which exhibits a jump across the interface. It may influence the mass conservation...

## Projects

Projects (2)

To design and analyse stabilised finite element methods for the equations of fluid mechanics.