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:
On a degenerate boundary value problem for relativistic magnetohydrodynamics with a general pressure law,
Zeitschrift für Angewandte Mathematik und Physik, (Springer), 75, 207 (2024).
- 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)
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
Softwares and skills
I have worked with following softwares and still learning some of them
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
Numerical Analysis
Functional Analysis
Learn maths on youtube
Non-Mathematical Books and shows
Novels
TV Series I recommend
Sci-fi and romcoms
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
Email:
rahul.barthwal@mathematik.uni-stuttgart.de
Call:
+49 711 685 65884