
Research Interests
 Oil and Gas Technlogy
 Vortex Induced Vibrations
 FluidSolid Interaction and Modeling and Interfacial Treatments
 Multimedium flow
 Parallel Computing
 Quantum Computation
 Fractional Calculus and Its Applications in Quantum Mechanics
 Applied Computational Mathematics
 Computational Quantum Mechanics
Publications

A. Kaboudian, B.C. Khoo, “The ghost solid methods for the elasticplastic solidsolid interactions”, Journal of Computational Physics, Under Review

A. Kaboudian, B.C. Khoo, “The ghost solid methods or solidsolid interactions”, Journal of Computational Physics, Vol. 257, Part A, pp. 102125, 15 January 2014.

P. Tavallali, A. Kaboudian, V.V. Kulish, “ Exact Solution for PhaseLagged Heat Equation in One Dimensional Domain”, Mathematics In Engineering Science and Aerospace, Vol. 4, No. 4, pp. 403413, 2013.
Research Experiences

Vortex Induced Vibrations of Flexible Risers (Current Research)
With the oil and gas exploration and production moving further offshore into deeper waters, one has to deal with new practical challenges every day. Long slender risers and moorings are subject to ocean currents which in turn lead to vortex shedding around these structures. The vortex shedding phenomenon causes vibration in the structure which can lead to fatigue and long term failure of the structures. Due to the high length of these risers, the phenomenon is inherently three dimensional in nature and the oscillatory load on the structure, as well as the structure response, is highly nonlinear. In this project, full CFD models for this complex and large scale problem are developed. The stabilized finite elements is used for fluid flow modeling and ALE is used for mesh motion. Finite element is used to calculate the structural deformations. The data obtained using the full CFD modelings can be used to further enhance semiempirical results.
I have been leading the development of our inhouse code which is developed in C, C++, and FORTRAN to implement all the discussed models. The large scale of the problem requires parallelization of the code for the timely completion of the computational jobs. We use OpenMP for our shared memory parallelization and MPI for message passing amongst our distributed nodes. Bash and Perl scripts are used for automation purposes. GMSH is used for mesh generation. By importing the mesh from GMSH, we are able to handle any complex geometrical shape for the domain, structure, and mesh.

The Ghost Solid Method for Elastic SolidSolid Interactions (Ph. D. Research Topic in NUS)
Elastic solidsolid interactions have many applications in various areas like biomedical research, nondestructive testing of solids, geophysical studies, and etc. In this research, three different variants of Ghost Solid Method have been proposed to capture the boundary conditions at the solidsolid interface of isotropic linearly elastic solids. The advantages and disadvantages of these methods have also been extensively studied through both analytical and numerical experiments. A method for prediction of nonphysical oscillations at the interface due to original ghost solid method is proposed. Two of the variants of the ghost solid method have been shown to be able to successfully remove these nonphysical oscillations. A method for extension of these methods to multidimensional settings has also been proposed. Results show acceptable agreements between the multidimensional and onedimensional results. Various possible boundary conditions at the interface, as in slip, noslip, friction, etc., are studied.

Phaselagged Formulation of Quantum Mechanics: Application to UltraFast Processes of Energy and Information Transport (M.Eng Research Topic at NTU)
The Schrödinger equation, the corner stone in quantum mechanics, gives rise to the paradox of instantaneous propagation of energy. The Schrödinger equation is not a relativistic formula. Despite of all the attempts, there is no unique and general formulation which removes the paradox and gives relativistic results in all cases has been proposed.
Three possible phasedlagged derivations of the Schrödinger equation have been proposed, based on the assumption that there exists a finite time lag between the onset of gradients and the corresponding flux. The extended version of the Schrödinger equation, therefore, has been proposed to eliminate the paradox of instantaneous propagation, intrinsic to the classical Schrödinger equation.
Furthermore, based on the theory of fractional calculus a fractional order PDE is proposed to modify the classical Schrödinger equation. The proposed equation has relativistic limits. New concepts such as quantum information wave speed has been proposed to further extend the idea of the Lorentz invariant.
 Solving Partial Differential Equations Using scilab (B. Sc theses in IUT)
In this project, we tried to solve PDEs, specifically heat equation, using scilab. Scilab is an open source software developed by INREA which has several matrix calculation abilities comparable to MATLAB. In the end of the project, a toolbox was designed for scilab which was named the PDE toolbox.
This project consisted of several programming stages:
The first stage was to develop an engine to generate mesh, apply boundary conditions and solve the corresponding PDE. This stage was implemented using the MODULEF which is a library of 3000 procedures written in FORTRAN 77. This part of the engine reads and write all the inputoutput data to files, so that all the data can be used for future reference and use. It also, performs all the computations to generate mesh, and solve the PDEs.
The second step was to interface the engine with the scilab engine so that the engine can be called inside scilab. This steps consisted of several steps of interfacing and calling either FORTRAN procedures or linux external programs inside scilab.
The third step was to develop a graphical user interface for the toolbox. This graphical user interface was developed using Tcl/Tk programming. The Tcl/Tk programs was later interfaced with scilab to facilitate inputoutput procedures.
The fourth step was to develop some tools for drawing the geometry or the domain of the solution. This step was done using the graphical properties of scilab. All drawing tools were designed within the scope of the project.The last stage was developing the post processing tool. In order to do so, post processing facilities and programs were developed using MODULEF library and were interfaced with the scilab engine.
