Edilbert Christhuraj

Applied and Computational Mathematics (ACoM)
RWTH Aachen University
Schinkelstr. 2
D-52062 Aachen
Germany

Room: 328b (Rogowski Building, 3rd floor)
Office Phone: +49 241 80-98671
Mobil Phone: +49 176 77182454
Email: Christhuraj@acom.rwth-aachen.de

• 01/20 – current: PhD Student at ACoM
  RWTH Aachen University, Aachen, Germany
• 05/19 – 10/19: Visiting student
  EPFL, Lausanne, Switzerland
• 04/16 – 10/19: Master of Science in Simulation Sciences (SiSc)
  RWTH Aachen University, Aachen, Germany
• 08/11 – 04/15: Bachelor of Engineering in Mechanical Engineering
  Anna University, Coimbatore, India

• 07/18 – 10/18: Guest Student: Extrapolated Stabilized Explicit Runge-Kutta methods
  Research centre Juelich, Juelich, Germany
• 05/17 – 05/18: Student Research Assistant: Aerodynamic Institute Aachen
  AIA, Aachen, Germany
• 05/15 – 08/15: Research Internship: Research Centre for Powder Metallurgy and Materials
  ARCI, Madras, India

Keywords: Numerical methods for non-equilibrium gas flows, moment methods, gas kinetic theory

<align justify> A wide range of real world problems is formulated in the form of partial differential equations, for example, heat transfer through a solid medium or flow through porous media. Often, these problems are stochastic in nature due to the presence of uncertainty or randomness in the system. In some cases, the mathematical model of the system is not in closed form. To solve such problem, one often uses discretization-based numerical methods such as finite difference or finite volume method. Over the years, many studies have proposed alternative methods. One of such alternatives is the stochastic formulation of a problem and stochastic solution methods. The presence of uncertainty in the problem provides a strong need to consider an approach that incorporates randomness into the numerical method. In this thesis, the stochastic solution algorithms for Burgers and incompressible Navier-Stokes equations are developed. Two approaches, particle-grid and particle-kernel approach, are used for developing the stochastic particle algorithms. These algorithms are demonstrated on one-dimensional Burgers and two-dimensional incompressible Navier-Stokes equations. Convergence studies are performed for each case.

Supervision: Hossein Gorji
Keywords: Stochastics, Particle methods, Fluid mechanics, Burgers' equation, Navier-Stokes
Download: final_copy_master_thesis_edilbert.pdf
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• Investigation of the CIP stabilization paramters and extension of the FencisR13 solver, Bachelor Thesis of Aditya Karthik, BITS PILANI, India, 2020.

• WS19/20: Numerical Methods for PDEs (SiSc) @ MathCCES, RWTH Aachen, with Prof. Krumscheid
• SS19: Mathematische Grundlagen II (CES) @ MathCCES, RWTH Aachen

• Solving Moment equations in kinetics gas theory using Fenics, MathCCES Lunch Seminar, RWTH Aachen, 12 January, 2021.
• Stochastic solution algorithms for Burgers and Navier-Stokes equations, Master Thesis Defense, RWTH Aachen, 28 October, 2019.
• ESERK- An ODE solver for stiff problems, Colloquium, Research Centre Julich, 28 September, 2018.