Peer reviewed publications

1. Arpit Babbar and Qifan Chen, "Compact Runge-Kutta Flux Reconstruction for Hyperbolic Conservation Laws with admissibility preservation", accepted in Journal of Scientific Computing. [Arxiv]
2. Sujoy Basak, Arpit Babbar, Harish Kumar and Praveen Chandrashekar, "Constraints Preserving Lax-Wendroff Flux Reconstruction for Relativistic Hydrodynamics with General Equations of State", accepted in Journal of Scientific Computing. [Arxiv]
3. Sujoy Basak, Arpit Babbar, Harish Kumar and Praveen Chandrashekar, "Bound preserving Lax-Wendroff flux reconstruction method for special relativistic hydrodynamics", Journal of Computational Physics (2025). [Arxiv], [Journal]
4. Arpit Babbar and Praveen Chandrashekar, "Lax-Wendroff Flux Reconstruction on adaptive curvilinear meshes with error based time stepping for hyperbolic conservation laws", Journal of Computational Physics (2025). [Arxiv], [Journal]
5. Arpit Babbar and Praveen Chandrashekar, "Multi-derivative Runge-Kutta flux reconstruction for hyperbolic conservation laws", Communications on Applied Mathematics and Computation (2025). [Arxiv], [Journal]
6. Arpit Babbar and Praveen Chandrashekar, "Generalized framework for admissibility preserving Lax-Wendroff Flux Reconstruction for hyperbolic conservation laws with source terms", Proceedings of International Conference on Spectral and High Order Methods (ICOSAHOM2023). [Arxiv], [Proceedings]
7. Arpit Babbar and Praveen Chandrashekar, "Lax-Wendroff Flux Reconstruction for advection-diffusion equations with error-based time stepping", Proceedings of International Conference on Spectral and High Order Methods (ICOSAHOM2023). [Arxiv], [Proceedings]
8. Arpit Babbar, Sudarshan Kumar Kenettinkara, Praveen Chandrashekar, "Admissibility preserving subcell limiter for Lax-Wendroff flux reconstruction", Journal of Scientific Computing, Vol. 99, Issue 2, May 2024 [Arxiv], [Journal]
9. Arpit Babbar, Sudarshan Kumar Kenettinkara and Praveen Chandrashekar, Lax-Wendroff flux reconstruction method for hyperbolic conservation laws, Journal of Computational Physics, Vol. 467, October 2022. [Arxiv], [Journal]

Preprints

1. Arpit Babbar, Valentin Churavy, Michael Schlottke-Lakemper, Hendrik Ranocha, "Automatic differentiation for Lax-Wendroff-type discretizations". [Arxiv]
2. Arpit Babbar and Praveen Chandrashekar, "Equivalence of ADER and Lax-Wendroff in DG/FR framework for linear problems". [Arxiv]

Talks

1. Compact Runge-Kutta Flux Reconstruction for non-conservative hyperbolic equations, Kompaktseminar 2025.
2. Single-stage time integration methods for hyperbolic partial differential equations, SCALES-2025.
3. Automatic differentiation and its application to Lax-Wendroff methods, invited talk at TIFR-CAM
4. IMEX compact Runge-Kutta Flux Reconstruction for hyperbolic equations, Arpit Babbar, Hendrik Ranocha, ICOSAHOM 2025, Mcgill University, Montreal, Canada
5. Compact Runge-Kutta methods for solving hyperbolic conservation laws, Arpit Babbar, Qifan Chen, ICOSAHOM 2025, Mcgill University, Montreal, Canada
6. Admissibility preserving IMEX Compact Runge-Kutta Flux Reconstruction, Arpit Babbar, Hendrik Ranocha, poster presentation at Numerical Methods for Hyperbolic Problems (numhyp) 2025
7. Compact Runge-Kutta methods for solving hyperbolic conservation laws, Oberseminar Mathematische Strömungsmechanik, Institut für Mathematik der Julius-Maximilians-Universität Würzburg
8. Admissibility preserving Lax-Wendroff Flux Reconstruction schemes for compressible flows, IGHASC: Indo-german Workshop on Hardware-aware Scientific Computing 2024, Heidelberg, Germany.
9. Compact Runge-Kutta Flux Reconstruction methods, Kompaktseminar 2024, Prien am Chiemsee, Germany.
10. Admissibility preserving Flux Reconstruction / Discontinuous Galerkin methods for compressible flows, Mathematics Of the Weather 2024, Bad Orb, Germany.
11. TrixiLW.jl: A high-order, single stage hyperbolic PDE solver using Trixi.jl, Arpit Babbar, Praveen Chandrashekar, invited to present in the Numerical Engine Room Talks
12. Domain-invariant subcell-based blending limiter for Lax-Wendroff Flux Reconstruction, Arpit Babbar, Praveen Chandrashekar, Sudarshan Kumar Kenettinkara, ICIAM August 20-25, 2023, Waseda Univ., Tokyo
13. Embedded error-based time stepping for Lax-Wendroff Flux Reconstruction for compressible flows, Arpit Babbar, Praveen Chandrashekar, ICOSAHOM, 14-18 August, 2023, Yonsei University, Seoul, Korea
14. Admissibility preserving subcell limiter for Lax-Wendroff flux reconstruction, Arpit Babbar, Praveen Chandrashekar, Sudarshan Kumar Kenettinkara, in MS6 Towards Practical High-Order Methods for Unsteady High-Fidelity Computational Fluid Dynamics, ICOSAHOM, 14-18 August, 2023
15. Error based time stepping for Lax-Wendroff Flux Reconstruction, Arpit Babbar, Praveen Chandrashekar, Indo-German conference on Computational Mathematics (IGCM), CDS IISc & IWR Heidelberg
16. Lax-Wendroff Flux Reconstruction for hyperbolic conservation laws, Arpit Babbar, Praveen Chandrashekar, Sudarshan Kumar Kenettinkara, during visit at IISER-Trivandrum

Thesis

1. “Lax-Wendroff Flux Reconstruction for Compressible Flows”, PhD thesis, Tata Institute of Fundamental Research - Centre for Applicable Mathematics, 2024. [PDF], [Source Code], [Cite].