Hyperbolic systems of conservation laws,
Asymptotic preserving schemes,
Genuinely multidimensional numerical schemes,
Nonlinear waves and shock waves.

Preprints
K. R. Arun, G. Bispen, M. Lukacova-Medvidova, and S. Noelle, IMEX large time step finite volume methods for low Froude number shallow water flows. Submitted.
K. R. Arun, and S. Noelle. An asymptotic preserving and well-balanced scheme for shallow flows, Submitted.
K. R. Arun, G. Chen, and S. Noelle. A finite volume evolution Galerkin scheme for acoustic waves in heterogeneous media, Submitted.
K. R. Arun, S. Noelle, M. Lukacova-Medvidova, and C.-D. Munz. An asymptotic preserving all Mach number scheme for the Euler equations of gas dynamics, Submitted.
K. R. Arun, and Phoolan Prasad. Propagation of a three-dimensional weak shock front using kinematical conservation laws, Submitted.
Published/Accepted in Journals
K. R. Arun, M. Lukacova-Medvidova, P. Prasad, and S. V. Raghurama Rao. A second order accurate kinetic relaxation scheme for inviscid compressible flows, Recent Developments in the Numerics of Nonlinear Hyperbolic Conservation Laws, Notes on Numerical Fluid Mechanics and Multidisciplinary Design, 2013, Volume 120/2013, 1-24 .
K. R. Arun, and M. Lukacova-Medvidova. A characteristics based genuinely multidimensional discrete kinetic scheme for the Euler equations. To appear in J. Sci. Comput.
K. R. Arun. A numerical scheme for three-dimensional front propagation and control of Jordan mode. SIAM J. Sci. Comput. 34:B148-B178, 2012.
K. R. Arun, and P. Prasad. Eigenvalues of kinematical conservation laws (KCL) based weakly nonlinear ray theory (WNLRT). Appl. Math. Comput. 217:2285-2288, 2010.
K. R. Arun, M. Lukacova-Medvidova, P. Prasad, and S. V. Raghurama Rao. An application of 3-D kinematical conservation laws: propagation of a three dimensional wavefront. SIAM J. Appl. Math. 70:2604–2626, 2010.
K. R. Arun, and P. Prasad. 3-D kinematical conservation laws (KCL): evolution of a surface in R³ - in particular evolution of a nonlinear wavefront. Wave motion. 46:293-311, 2009.
K. R. Arun, M. Kraft, M. Lukacova-Medvidova, and P. Prasad. Finite volume evolution Galerkin method for hyperbolic conservation laws with spatially varying flux functions. J. Comput. Phys. 228:565-590, 2009.
Conference Proceedings
K. R. Arun, M. Lukacova-Medvidova, and P. Prasad. Numerical Front Propagation Using Kinematical Conservation Laws. In Finite Volumes for Complex Applications VI Problems & Perspectives (Prague, 2011), pp. 49-57, Springer Proceedings in Mathematics, Vol. 4, 2011.
K. R. Arun, and Phoolan Prasad, Kinematical conservation laws (KCL): equations of evolution of curves and surfaces. Mathematics in science and technology, 2044, World Sci. Publ., Hackensack, NJ, 2011.
K. R. Arun, S. V. Raghurama Rao, M. Lukacova-Medvidova, and P. Prasad. A genuinely multidimensional relaxation scheme for hyperbolic conservation laws. In proceedings of the seventh Asian CFD conference, Bangalore, India, pp. 1029-1039 (electronic).

The Martin Forster Medal for the best thesis in Mathematical Sciences for the year 2010-2011, Indian Institute of Science, Bangalore, March 2012.
Alexander von Humboldt Fellowship to do postdoctoral research at the Institut fuer Geometrie und Praktische Mathematik, RWTH-Aachen University, Germany, July 2010.
Junior Research Associateship, Indian Institute of Science, Bangalore, May 2010 - October 2010.
DST-DAAD joint research grant to visit the Institut fuer Numerische Simulation, Technische Universitaet Hamburg-Harburg, Germany, 2006 and 2007.
Joint CSIR-UGC NET Examination, December 2005, Qualified with Junior Research Fellowship.
Research Scholarship, Indian Institute of Science, Bangalore, 2005- 2006.
Qualified GATE-2004.
Merit Scholarship, Indian Institute of Technology Madras, 2002-2004.
University First Rank, B.Sc. Mathematics, Mahatma Gandhi University, Kottayam, 2002.