Deepak Bhoriya

About Me

At present, I am working as a Post-Doctoral Researcher in the Department of Physics and Astronomy, University of Notre Dame, Indiana, USA. I work in collaboration with Prof. Dinshaw S. Balsara. My most of the research work emphasises on the Mathematical aspects of the astrophysical flows, which includes but not limited to, the designing of high-order finite difference and finite volume schemes for the numerous hyperbolic conservation laws. Some of my research also covers the hyperbolic systems with non-conservative products. Before coming to Indiana, I was working as a research scholar in the Department of Mathematics, Indian Institute of Technology (IIT-Delhi), India. There, I obtained my Doctor of Philosophy (Ph.D.) degree in the year 2022. I worked under the supervision of Prof. Harish Kumar, one of the finest guide and human being I have ever met in my research journey. At IIT-Delhi, the principal research work was established on the relativistic flows in the hydrodynamics and two-fluid plasma regimes. My thesis title "Entropy Stable Schemes for Relativistic Flows" explains the same.

To see more about my research work, one can visit the Publication Section, or alternatively, one can see my published work on the ResearchGate and Google scholar profile.

Employment

May, 2022 - present Post-Doctoral Research Associate

- University of Notre Dame, Notre Dame, 46556, USA.

Education

2017 - 2022 Ph.D. Mathematics
- Department of Mathematics, IIT-Delhi, New-Delhi, India.
- Supervisor: Prof. Harish Kumar.
- Thesis Title: "Entropy Stable Schemes for Relativistic Flows" 2015 - 2017 Masters of Science (M.Sc.) in Mathematics
- Department of Mathematics , IIT-Bombay, Mumbai, India. 2012 - 2015 Bachelor of Science (B.Sc.) in Mathematics
- Sri Venkateswara College, University of Delhi, New-Delhi, India. 2010 - 2012 High-School (Medical Science with Mathematics)
- Shri Daulat Ram Public School, New-Delhi, India.

Research Interest

High-order schemes for hyperbolic systems with non-conservative products (Baer-Nunziato, Debris Flows, etc.) Numerical Methods (finite-difference, finite-volume and Discontinuous galerkin) and Analysis of Hyperbolic PDEs. Computational Fluid dynamics and Plasma Flows. Entropy Stable Schemes. GPU computing in ADER-Based schemes using OPENACC. Compututation interests: Parallel computing using CPUs (MPI, OPENMP) and GPUs (OPENACC).

Publications

Published / Accepted:

Bhoriya, D., Biswas, B., Kumar, H., Chandrashekhar, P., Entropy stable discontinuous Galerkin schemes for two-fluid relativistic plasma flow equations. Journal of Scientific Computing, 97(3), 72 (2023). https://doi.org/10.1007/s10915-023-02387-z Yadav, A., Bhoriya, D., Kumar, H., Chandrashekar, P., Entropy stable schemes for the shear shallow water model Equations. Journal of Scientific Computing, 97(3), 77 (2023). https://doi.org/10.1007/s10915-023-02374-4 Bhoriya, D., Kumar, H., Chandrashekar, P., High-order finite-difference entropy stable schemes for two-fluid relativistic plasma flow equations, Journal of Computational Physics 488, (2023) 112207. https://doi.org/10.1016/j.jcp.2023.112207 Balsara, D., Bhoriya, D., Shu C.-W., Kumar, H. Efficient Finite Difference WENO Scheme for Hyperbolic Systems with Non-Conservative Products, Communications on Applied Mathematics and Computation (2023). https://doi.org/10.1007/s42967-023-00275-9 Subramanian, S., Balsara, D., Bhoriya, D., Kumar, H., Techniques, Tricks and Algorithms for Efficient GPU-Based Processing of Higher Order Hyperbolic PDEs , Communications on Applied Mathematics and Computation (2023). https://doi.org/10.1007/s42967-022-00235-9 Biswas, B., Kumar, H., Bhoriya, D., Entropy stable discontinuous Galerkin schemes for the special relativistic hydrodynamics equations, Computers & Mathematics with Applications, 112, 55-75 (2022). https://doi.org/10.1016/j.camwa.2022.02.019 Bhoriya, D., Kumar, H., Entropy-stable schemes for relativistic hydrodynamics equations, Z. Angew. Math. Phys. (ZAMP) 71, 29 (2020). https://doi.org/10.1007/s00033-020-1250-8 Balsara, D., Bhoriya, D., Shu C.-W., Kumar, H. Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Conservation Laws, Communications on Applied Mathematics and Computation (2023). (Accepted) Balsara, D., Bhoriya, D., Shu C.-W., Kumar, H. Efficient Alternative Finite Difference WENO Schemes for Hyperbolic Systems with Non-Conservative Products, Communications on Applied Mathematics and Computation (2023). (Accepted)

Submitted:

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TA Ship / Teaching

Teaching assistant for the course MTL100-Calculus(B.Tech. 1st year)(twice). Teaching assistant for the course MTL101-Linear-Algebra(B.Tech. 1st year)(thrice). Teaching assistant for the course Real Analysis(M.Sc. 1st year).