Raushan Kumar currently serves as Assistant Professor at the Department of Mechanical Engineering, School of Engineering, Amrita Vishwa Vidyapeetham, Coimbatore Campus.


  • 2019 : Ph. D.,
    IIT Guwahati


Publication Type: Journal Article

Year of Publication Title


Raushan Kumar and Anoop K. Dass, “A new flux-limiting approach–based kinetic scheme for the Euler equations of gas dynamics”, International Journal for Numerical Methods in Fluids, vol. 90, pp. 22-56, 2019.[Abstract]

Summary This paper proposes a new kinetic-theory-based high-resolution scheme for the Euler equations of gas dynamics. The scheme uses the well-known connection that the Euler equations are suitable moments of the collisionless Boltzmann equation of kinetic theory. The collisionless Boltzmann equation is discretized using Sweby's flux-limited method and the moment of this Boltzmann level formulation gives a Euler level scheme. It is demonstrated how conventional limiters and an extremum-preserving limiter can be adapted for use in the scheme to achieve a desired effect. A simple total variation diminishing criteria relaxing parameter results in improving the resolution of the discontinuities in a significant way. A 1D scheme is formulated first and an extension to 2D on Cartesian meshes is carried out next. Accuracy analysis suggests that the scheme achieves between first- and second-order accuracy as is expected for any second-order flux-limited method. The simplicity and the explicit form of the conservative numerical fluxes add to the efficiency of the scheme. Several standard 1D and 2D test problems are solved to demonstrate the robustness and accuracy.

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Publication Type: Conference Paper

Year of Publication Title


Raushan Kumar and Dass, A., “A New High-Resolution Kinetic Flux-Corrected Scheme on Unstructured Grids for 2D Euler Equations of Gas Dynamics”, in 7th International and 45th National Conference on Fluid Mechanics and Fluid Power (FMFP), IIT Bombay, Mumbai, India, 2018.[Abstract]

This paper proposes a new high-resolution kinetic flux-corrected scheme for the Euler equations of gas dynamics. A flux-corrected scheme for the collisionless Boltzmann equation is formulated first and the moment of this discretized scheme gives an Euler level scheme. This Euler level scheme is solved normal to the cell faces on unstructured grids using the rotational invariance property of the 2D Euler equations which provides numerical fluxes. The scheme does not require calculation of split fluxes for upwinding and no error functions need to be calculated as is the case with KFVS type schemes. This simplicity of the scheme makes it very cost effective for unstructured grid calculations. The numerical results shown demonstrate the robustness and accuracy of the scheme.

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Raushan Kumar and Anoop K. Dass, “A New Second Order Accurate Kinetic Theory Based Scheme for Euler Equations”, in 5th International and 41st National Conference on Fluid Mechanics and Fluid Power, IIT Kanpur, 2014.