Research

My research interests include:

• High-order numerical schemes for hyperbolic conservation laws
• Structure preservation of numerical methods
• Active flux method
• Nonlocal conservation laws
• Conservation laws with discontinuous flux
• Rigorous convergence and stability analysis of numerical schemes

Publications / Preprints

• A convergent MUSCL-Hancock scheme for non-local conservation laws
  Nikhil Manoj, G.D. Veerappa Gowda and Sudarshan Kumar K.
  (to appear in ESAIM: M2AN, 2026).
  https://doi.org/10.1051/m2an/2026060
• A positivity preserving second-order scheme for multi-dimensional system of non-local conservation laws
  Nikhil Manoj, G.D. Veerappa Gowda, Sudarshan Kumar K.
  Zeitschrift für angewandte Mathematik und Physik (2026).
  https://link.springer.com/article/10.1007/s00033-026-02742-8
• Convergence analysis of a MUSCL-type central scheme for conservation laws with discontinuous flux
  Nikhil Manoj and Sudarshan Kumar K.
  IMA Journal of Numerical Analysis (2025).
  https://doi.org/10.1093/imanum/draf136
• Convergence of a second-order scheme for non-local conservation laws
  Nikhil Manoj, G.D. Veerappa Gowda and Sudarshan Kumar K.
  ESAIM: M2AN, 57(6), 3439–3481 (2023).
  https://www.esaim-m2an.org/articles/m2an/abs/2023/06/m2an230129/m2an230129.html

Thesis

• Numerical approximation of conservation laws with non-local and discontinuous fluxes
  Ph.D. thesis (2025).

Talks

• A provably convergent MUSCL-type central scheme for conservation laws with discontinuous flux
  Hyperbolic Problems: Theory, Numerics and Applications (HYP2026),
  University of Stuttgart, Germany, May 25–29, 2026.
• A convergent MUSCL–Hancock scheme for nonlocal conservation laws
  Contributed talk at Hyperbolic Problems: A Comprehensive Approach,
  University of Würzburg, Germany, March 23–27, 2026.
• On the numerical approximation of non-local conservation laws (via Zoom)
  Oberseminar Mathematische Strömungsmechanik,
  Institut für Mathematik, Julius-Maximilians-Universität Würzburg, Germany, Sept. 18, 2025.
• Convergence of a second-order scheme for non-local conservation laws
  Contributed talk at EQUADIFF 2024,
  Karlstad University, Sweden, June 10–14, 2024.