Rahul Barthwal

I'm a postdoctoral researcher of Applied Mathematics

About

Welcome! Currently, I am working as a postdoctoral researcher at the Institute of Applied Analysis and Numerical Simulation, University of Stuttgart under the mentorship of Prof. Christian Rohde. Prior to this, I completed my PhD at the Department of Mathematics, Indian Institute of Technology Kharagpur under the supervision of Dr. T. Raja Sekhar. My broad area of research is analysis of hyperbolic partial differential equations. I mostly work in applied mathematics, including the study of gas dynamics, thin film flows, astrophysics, shallow water equations and related areas. To see more about my research work one can click on the research button or alternatively, can see my published works on the Researchgate and Google Scholar profile (links given below). I am always happy to talk about my research. Please feel free to reach out to me through the email/links below.

Postdoctoral Researcher.

Institute of Applied Analysis and Numerical Simulation, University of Stuttgart

In the group of Prof. Christian Rohde

  • Birthday: 23 August 1995
  • Phone: +49 711 685 65884
  • City: Stuttgart, Germany
  • Age: 29
  • Degree: Ph.D.
  • Email: rahul.barthwal@mathematik.uni-stuttgart.de

Research Interests: I am currently working on the Analysis and development of Hyperbolic Conservation Laws. Hyperbolic conservation laws deeply demonstrate the essence of sophisticated physical phenomena. A major difficulty in this regard is that discontinuities may appear in the solution of nonlinear hyperbolic conservation laws even though the initial data is very smooth. My current project of study is the analysis of certain initial and boundary value problems for the different classes of one and more dimensional hyperbolic conservation laws describing physical phenomena such as thin film flows, gas flows, traffic flows, and several other conservative systems. In particular, I have worked on developing solutions to several initial and boundary value problems for sonic-supersonic patches occurring frequently in the transonic flows and gas expansion problems through a sharp corner for multi-dimensional potential flow equations. I have also analyzed some purely hyperbolic multi-dimensional systems while studying their nonlinear wave interactions. I am also interested in analyzing the multi-phase counterparts of the above systems which involve a higher number of primitive variables and describe the physics of the problems in a more realistic manner. Currently, I am working on developing numerical schemes and analyzing their theoretical aspects in the context of conservation laws and also learning the tools of Data-driven modelling and control problems from the viewpoint of conservation laws. In future, I would like to study the turbulence models and would try to develop numerical schemes for such complicated models.

Publications

This is my list of publications. Most of them are available on arXiv, if you need a published version of any of the papers, do not hesitate to contact me.

  • Rahul Barthwal and T. Raja Sekhar: Existence of solutions to gas expansion problem through a sharp corner for 2-D Euler equations with general equation of state. In: Studies in Applied Mathematics, MIT Journal (Wiley), 151 (1), 141-170, (2023).
  • Rahul Barthwal, T. Raja Sekhar and G. P. Raja Sekhar: Construction of solutions of a two-dimensional Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution. In: Mathematical Methods in the Applied Sciences, (Wiley), 46 (6), 7413-7434, (2023).
  • Rahul Barthwal and T. Raja Sekhar: Existence and regularity of solutions of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow with general equation of state. In: Journal of Mathematical Analysis and Applications (Elsevier) 523 (2), 127022, (2023).
  • Rahul Barthwal and T. Raja Sekhar: Two-dimensional non self-similar Riemann solutions for a thin film model of a perfectly soluble anti-surfactant solution. In: Quarterly of Applied Mathematics (American Mathematical Society), 80(4), 717-738, (2022).
  • Rahul Barthwal and T. Raja Sekhar: On the existence and regularity of solutions of semi-hyperbolic patches to 2-D Euler equations with van der Waals gas. In: Studies in Applied Mathematics, MIT Journal (Wiley), 148(2), 543-576, (2022).
  • Rahul Barthwal and T. Raja Sekhar: Simple waves for two-dimensional magnetohydrodynamics with extended Chaplygin gas. In: Indian Journal of Pure and Applied Mathematics (Springer), 53, 542-549, (2022).

    • Communicated and ongoing research works

    These are some of the works under review and some works that I am currently working on.

  • Rahul Barthwal, Christian Rohde and Yue Wang, Generalized Riemann solver to a two-phase thin film model with a perfectly soluble anti-surfactant, In preparation.
  • Rahul Barthwal and Christian Rohde, Convergence of an operator-splitting Lax-Friedrichs scheme for the Burgers-Hilbert equation, In preparation.
  • Anamika, Rahul Barthwal and T. Raja Sekhar: Construction of solutions to a Riemann problem for a two-dimensional Keyfitz-Kranzer type model governing thin film flow, (December 2023)
  • Rahul Barthwal and T. Raja Sekhar: On a degenerate boundary value problem for relativistic magnetohydrodynamics with a general pressure law, (July 2023),arXiv: 2306.13974

    • Curriculam Vitae

    This is my express curriculum vitae. Here is a link to my full curriculum vitae .

    Summary

    Rahul Barthwal

    Postdoctoral researcher in the field of Hyperbolic conservation laws: Theory, modelling and Numerics with 1+ year of experience.

    Supervisor: Prof. Christian Rohde

    • Universität Stuttgart, Stuttgart, Germany
    • +49 711 685 65884
    • rahul.barthwal@mathematik.uni-stuttgart.de

    Education

    Ph.D. in Applied Mathematics

    2018 - 2023

    Indian Institute of Technology, Kharagpur, India

    Thesis Title: "Nonlinear Aspects of Certain Multi-dimensional Hyperbolic System of Conservation Laws"

    Supervisor: Dr. T. Raja Sekhar

    Master of Science in Mathematics and Scientific Computing

    2015 - 2017

    Motilal Nehru National Institute of Technology, Allahabad, India

    Thesis Title: "Magnetogasdynamics Shock Wave in a Rotating Non-Ideal Gas with Conduction Radiation Heat Flux."

    Bachelor of Science

    2012- 2015

    Hemwati Nandan Bahuguna Garhwal University, Srinagar, India

    Professional Experience

    Postdoctoral Researcher of Applied Mathematics

    July 2023 - Present

    Supervisor: Prof. Christian Rohde

    University of Stuttgart, Stuttgart, Germany

    • Working on several systems of conservation laws and developed numerical schemes for them
    • Lecturer and instructor for the Master's course "Numerical methods for differential equations". Received feedback of 1.6 out of 5, 1 being the best and 5 being the worst.
    • Developed mathematical models for fluid dynamical phenomena and analyzed them.
    • Teaching assistant for Höhere Mathematik 3: Winter semester 2023

    Assistant Professor

    July 2017 - April 2018

    Smt. S. R. Patel Engineering College, Unjha, Gujarat

    Awards

    IMS Award for best paper presentation

    88th Annual Conference of Indian Mathematical Society held at BIT-Mesra for presenting "Study of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow".

    Travel grant (1000 Euro)

    Institute of Applied Analysis to attend the summer school "Horizons in Nonlinear PDEs", Ulm University, Germany.

    DST international travel grant award

    To attend the summer school "Horizons in Nonlinear PDEs", Ulm University, Germany (Not availed).

    Young Scientist Award

    66th Congress of Indian Society Of Theoretical and Applied Mechanics(ISTAM) held at VIT-AP University for presenting "A two-dimensional Riemann problem for a new hyperbolic thin film model of a perfectly soluble anti-surfactant solution".

    Silver Medalist in M.Sc. Mathematics and Scientific Computing.

    Deendayal Upadhyay excellency in education award for securing 9th Rank in state board's senior secondary exam.

    Scholarships

    UGC-CSIR Senior research fellowship

    September, 2021 - June, 2023

    Indian Institute of Technology Kharagpur

    UGC-CSIR Junior research fellowship

    August, 2019 - August, 2021

    Indian Institute of Technology Kharagpur

    Teaching assistantship

    July, 2018 - August, 2019

    Indian Institute of Technology Kharagpur

    INSPIRE Scholarship

    July, 2012 - July, 2017

    Ministry of Human Resources and Development, India

    Workshops, Conferences and Invited talks

    List of workshops, seminars, and conferences I attended. Also, the list of invited talks where I delivered a lecture/talk.

    • All
    • Conferences
    • Workshops
    • Invited talks
    • Organization
    Delivered an invited talk on On the convergence of an operator-splitting Lax-Friedrichs scheme for Burgers-Hilbert equation in Department of Mathematics, Indian Institute of Technology Delhi, July 31, 2024.
    19th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2024), SJTU, Shanghai, China, On the convergence of an operator-splitting Lax-Friedrichs scheme for Burgers-Hilbert equation, July 01-05, 2024.
    SPP Workshop on Analysis of Dissipation in Inviscid and Compressible Fluid Dynamics , University of Konstanz, Konstanz, June 5-7 2024.
    Delivered an invited talk On a class of sonic-supersonic boundary value problems in an Online PDE workshop conducted by the University of Oslo, Norway, October 31, 2023.
    Sino-German Workshop on Advanced Nonlinear Methods for Hyperbolic Balance Laws , Beijing, China ``Study of supersonic-sonic patch for axisymmetric relativistic transonic flow", September 25-28, 2023.
    16th Workshop on Conservation laws, Hirschegg, Austria, On a supersonic-sonic patch for axisymmetric relativistic Euler equations, September 10-16, 2023.
    88th Annual Conference of Indian Mathematical Society BIT, Mesra,Study of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow December 27-30, 2022.
    67th Congress of Indian Society Of Theoretical and Applied Mechanics(ISTAM) IIT, Mandi, December 14-16, 2022.
    NCM workshop on Control Theory for Differential Equations , IISER, Kolkata, November 28-December 10, 2022.
    Delivered an invited lecture on Nonlinear wave interactions in certain hyperbolic systems of conservation laws in Institute of Applied Analysis and Numerical Simulation, University of Stuttgart, Stuttgart, October 4, 2022.
    Summer school Horizons in Nonlinear PDEs , Institute of Applied Analysis, Ulm University, Existence and regularity of solutions of a supersonic-sonic patch arising in axisymmetric relativistic transonic flow, September 26-30, 2022.
    18th International Conference on Hyperbolic Problems: Theory, Numerics, Applications (HYP2024) University of Malaga, Malaga, Spain, Construction of solutions of a two-dimensional Riemann problem for a thin film model of a perfectly soluble anti-surfactant solution, June 20-24, 2022.
    66th Congress of Indian Society Of Theoretical and Applied Mechanics(ISTAM) VIT-AP University, Amravati, A two-dimensional Riemann problem for a new hyperbolic thin film model of a perfectly soluble anti-surfactant solution, December 3-5, 2021.
    64th Congress of Indian Society Of Theoretical and Applied Mechanics(ISTAM) IIT Bhubaneshwar, Bhubaneshwar Simple waves for two-dimensional magnetohydrodynamics with extended Chaplygin gas, December 9-12, 2019.
    NCM workshop on System of Conservation Laws: Theory and Numerics , Tata Institute of Fundamental Research Center for Applicable Mathematics, Bengaluru, August 5-17, 2019.
    GIAN course on Kinetic Theory of Non-Equilibrium Gas Flows: Theory and Computations , Indian Institute of Technology Madras, December 10-14, 2018.

    Softwares and skills

    I have worked with following softwares and still learning some of them

    LAtex 90%
    Office 90%
    Matlab 80%
    Python 80%
    Maple 70%
    Mathematica 70%

    Miscellaneous

    Here are some information that might be useful to you. I list some books and learning links that I really like, some non-mathematical stuff that interests me, and some stuff that I like!

    Mathematical Books and online links

    Hyperbolic Partial diffrential equations

  • Partial diffrential equations, L. C. Evans: Covers all the basics of partial differential equations and covers basics for Hyperbolic PDEs and conservation laws.
  • Hyperbolic Conservation laws in Continumm physics, C. M. Dafermos: Its a bible of conservation laws
  • Numerical Approximation of Hyperbolic Systems of Conservation Laws, E. Godlweski and P. A. Raviart: Covers all the basics of systems of conservation laws while describing the numerics as well
  • Hyperbolic systems of conservation laws: the one-dimensional Cauchy problem, Alberto Bressan: An intersting read to understand the theory in detail
  • The two-dimensional Riemann problem in gas dynamics, J. Li: Best book to understand the two-dimensional Riemann problems for compressible flow
    •  

    Numerical Analysis

  • Numerical Analysis, Richard L. Burden, J. Douglas Faires: Covers all the sections of introductory Numerical Analysis
  • Riemann solvers and numerical methods for fluid dynamics: a practical introduction, E. F. Toro: Bible for the numerical schemes and their implementation
  • Numerical methods for conservation laws, R. J. Leveque: Best book to understand the finite volume schemes and their implementation
    •  

    Functional Analysis

  • Sobolev Spaces, John J. F. Fournier and Robert A. Adams: Covers Functional Analysis
  • Topics in Functional Analysis and Applications, S. Kesavan: Covers Functional Analysis required for FEM
    •  

    Learn maths on youtube

  • 3Blue1Brown
  • Numberphile
  • NPTEL HRD
  • MIT OpenCourseWare
  • BlackPenRedPen
  • The Bright Side of Mathematics
  • Dr Peyam
    •  

    Non-Mathematical Books and shows

    Novels

  • Kitne Pakistan, Kamleshwar
  • Shiva Trilogy, Amish
  • Da Vinci Code, Angels and Demons, Dan Brown
  • Raag Darbari, Shrilal Shukl
  • Godaan, Gaban, Premchand
    •  

    TV Series I recommend

    Sci-fi and romcoms

  • Dark, Netflix
  • Big Bang Theory, Netflix
  • Band of Brothers, HBO
  • Friends, Netflix
  • Game of thrones, HBO
  • House of Cards, Netflix
  • Breaking Bad, Netflix
  • Mindhunters, Netflix
    •  

    Some of my other interests

    Apart from the aforementioned things, I am also a big badminton fan and love to play badminton doubles and watching badminton games. I also love to abstract out my emotions in the form of poetries at times. Some of my favourite poetry forms are geet, ghazal and nazm. Some of my favourite poets are Ghalib, Meer, Ahmad Faraz, Bashir Badr, Jaun elia, Dushyant Kumar etc.

    Testimonials

    These are some of the comments from the attendees of the course "Numerical methods for differential equations" and my supervisors

    Anonymous

    Student, University of Stuttgart

    The teaching was the best part of the course. Rahul makes sure to explain every concept in detail considering students perspective.

    Anonymous

    Student, University of Stuttgart

    The course is structured in a very comprehensible and efficient manner, which helps in easy understanding of the concepts.

    Anonymous

    Student, University of Stuttgart

    The contents are conveyed in an understandable manner, and the exercises and assignments help visualize the taught concepts.

    Anonymous

    Student, University of Stuttgart

    The approach and delivery of the professor/lecturer is excellent and I was able to understand the content well. The mathematics was explained in a very understandable manner and the professor/lecturer made sure that the material was easy to grasp and we could be confident in studying and learning it. I really enjoyed the courrse and attending classes because of the atmosphere created by the professor. One of my favorite professors here!

    Anonymous

    Student, University of Stuttgart

    It is great to learn about the theoretical background behind numeric methods and the course content is very interesting.

    Anonymous

    Student, University of Stuttgart

    I liked the way the things were explained. It was clear and concise.

    Contact

    If you have any questions, please feel free to write to me. If I don't respond, don't feel guilty and send me a reminder.

    Location:

    Universität Stuttgart, Stuttgart, Germany

    Call:

    +49 711 685 65884

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