Ritesh Kumar Dubey
@srmist.edu.in
Associate Professor
SRM Institute of Science and Technology
RESEARCH INTERESTS
Numerical analysis, scientific computing and deep learning
Scopus Publications
Scopus Publications
Prabhat Mishra and Ritesh Kumar Dubey
IOP Publishing
Abstract This work presents an improved version of non-linear weight limiters to obtain third order non-oscillatory WENO scheme. The construction of this modified weight limiter is based on fuzzy inference system, which is a knowledge based rule system. The linear combination of overlapped basis functions is used to achieve the optimized weight limiters by exploring the linguistics hedges operator on the basis functions. The WENO scheme using optimized weight limiter achieves third order of accuracy and gives higher resolution to discontinuities compared to other established third order WENO schemes.
Ritesh Kumar Dubey
Walter de Gruyter GmbH
Abstract This work frames the problem of constructing non-oscillatory entropy stable fluxes as a least square optimization problem. A flux sign stability condition is defined for a pair of entropy conservative flux (F∗ ) and a non-oscillatory flux (Fs ). This novel approach paves a way to construct non-oscillatory entropy stable flux (F̂) as a simple combination of (F∗ and Fs ) which inherently optimize the numerical diffusion in the entropy stable flux (F̂) such that it reduces to the underlying non-oscillatory flux (Fs ) in the flux sign stable region. This robust approach is (i) agnostic to the choice of flux pair (F∗, Fs ), (ii) does not require the computation of costly dissipation operator and high order reconstruction of scaled entropy variable to construct the diffusion term. Various non-oscillatory entropy stable fluxes are constructed and exhaustive computational results for standard test problems are given which show that fully discrete schemes using these entropy stable fluxes do not exhibit nonphysical spurious oscillations in approximating the discontinuities compared to the non-oscillatory schemes using underlying fluxes (Fs ) only. Moreover, these entropy stable schemes maintain the formal order of accuracy of the lower order flux in the pair.
Vikas Kumar Jayswal, Prashant Kumar Pandey, and Ritesh Kumar Dubey
Springer Science and Business Media LLC
Vikas Kumar Jayswal and Ritesh Kumar Dubey
Springer Science and Business Media LLC
Prashant Kumar Pandey and Ritesh Kumar Dubey
Elsevier BV
Ritesh Kumar Dubey and Prabhat Mishra
Wiley
It is well known that on uniform mesh classical higher order schemes for evolutionary problems yield an oscillatory approximation of the solution containing discontinuity or boundary layers. In this article, an entirely new approach for constructing locally adaptive mesh is given to compute nonoscillatory solution by representative “second” order schemes. This is done using modified equation analysis and a notion of data dependent stability of schemes to identify the solution regions for local mesh adaptation. The proposed algorithm is applied on scalar problems to compute the solution with discontinuity or boundary layer. Presented numerical results show underlying second order schemes approximate discontinuities and boundary layers without spurious oscillations.
C. R. Jisha and Ritesh Kumar Dubey
Springer Science and Business Media LLC
C.R. Jisha, T.K. Riyasudheen, and Ritesh Kumar Dubey
Elsevier BV
Jisha CR, Ritesh Kumar Dubey, Dudley Benton, and Rashid A
IOP Publishing
Abstract The Kudryashov and Sinelshchikov (KS) equation address pressure waves in liquid-gas bubble mixtures while considering heat transport and viscosity. This study mainly includes two types of generalized solutions: polynomial function traveling wave solutions and rational function traveling wave solutions. In this study, we constructed the KS equation’s exact traveling and solitary wave solutions with variable coefficients by the generalized unified method (GUM). These newly created solutions play a significant role in mathematical physics, optical fiber physics, plasma physics, and other applied science disciplines. We illustrated the dynamical behavior of the discovered solutions in three dimensions. We proposed the possibility of discussing wave interaction and other wave structures using bilinear form related to the Hirota method for the fractional solutions.
Prabhat Mishra, Vikas Gupta, and Ritesh Kumar Dubey
American Institute of Mathematical Sciences (AIMS)
<p style='text-indent:20px;'>In this work a novel mesh adaptation technique is proposed to approximate discontinuous or boundary layer solution of partial differential equations. We introduce new estimator and monitor function to detect solution region containing discontinuity and layered region. Subsequently, this information is utilized along with equi-distribution principle to adapt the mesh locally. Numerical tests for numerous scalar problems are presented. These results clearly demonstrate the robustness of this method and non-oscillatory nature of the computed solutions.</p>
Prashant Kumar Pandey, Farzad Ismail, and Ritesh Kumar Dubey
Springer Science and Business Media LLC
Vikas Gupta, Sanjay K. Sahoo, and Ritesh K. Dubey
Springer Science and Business Media LLC
Sabana Parvin and Ritesh Kumar Dubey
Wiley
A new simple and generic framework is proposed to construct nonlinear weights for third‐order weighted essentially nonoscillatory scheme (WENO) reconstructions. It is done by imposing necessary conditions on nonlinear weights to get a nonoscillatory WENO scheme. These conditions give further insight into the required structure of nonlinear weights to design third‐order WENO schemes. This new framework for WENO weights is completely different from the existing prevailing approaches. Several nonlinear weights using different functions of a smoothness parameter (termed as weight limiter functions) are proposed and analyzed. These new weights by construction guarantee for third‐order accurate nonoscillatory scheme. Numerical results for various benchmark test problems are given and compared with WENO‐JS3 wnd WENO‐Z3 scheme. Computational results show that WENO schemes using proposed weights achieves third‐order accuracy for smooth solution and resolves discontinuities without spurious oscillations.
Parvin Sabana and Dubey Ritesh Kumar
AIP Publishing
High order accurate shock-capturing ENO schemes are mainly based on high order ENO reconstructions. Generally, classical ENO reconstruction methods show some relevant drawbacks. In this paper, we introduce a new ENO reconstruction procedure, the TVENO methods, to design high order accurate shock capturing methods for hyperbolic conservation laws, in order to overcome the drawbacks of classical ENO procedure. The main features of these new ENO method is that it substantially reduced smearing near discontinuities and gives a good resolution of corners and local extrema. Computational results of several one-dimensional numerical experiments for scalar conservation laws, including linear advection, Burger’s equation are given in support of our claim.
Mishra Prabhat and Dubey Ritesh Kumar
AIP Publishing
In this work a novel moving mesh technique is proposed to approximate discontinuity (shock, rarefaction wave). We introduce new estimator function to capture the solution region and monitor function to reconstruct the mesh-points incorporate with equi-distribution principle. The robustness of the algorithmic approach is presented on numerical section.
Ritesh Kumar Dubey, Anupam Gupta, Vikas Kumar Jayswal, and Prashant Kumar Pandey
Springer Singapore
Shruti Dubey and Ritesh Kumar Dubey
Springer Science and Business Media LLC
Biswarup Biswas and Ritesh Kumar Dubey
Elsevier BV
Ritesh Kumar Dubey and Vikas Gupta
World Scientific Pub Co Pte Lt
A robust automated mesh refinement algorithm is proposed for numerical solution of singularly perturbed boundary and interior layer problems. The proposed algorithm is heuristically based on two smoothness indicators which are functions of consecutive differences of the computed solution on a given mesh. The main salient features of the proposed heuristic mesh generation algorithm are: (i) it does not require a priori knowledge about the nature or location of the layered region, (ii) it is independent of the problem under consideration and the underlying numerical scheme. The proposed algorithm is applied to solve a wide range of 1D as well as 2D test problems to show its robustness.
Neelesh Kumar and Ritesh Kumar Dubey
Springer Science and Business Media LLC
Ritesh Kumar Dubey
Informa UK Limited
Many complex physical processes in engineering and technology can be modelled as systems of ordinary or partial differential equations. Examples of area where such differential models arise are ubiquitous e.g., multiphase flow, shape optimization, fluid flow control, gas-dynamics, finance, industrial mixing processes and biological processes etc. It is desired as well a need to better understand such complex physical processes through the solution of such differential equations model. It leads to futher refinement and development of new mathematical models along with the solution techniques. These solution technique can be analytical or computational in nature. This special issue on Nonlinear differential equations – theory, computations and applications of CMES focuses on advances on the numerical techniques, finite-element and finite difference methods for specific ordinary and partial differential equations along with dynamical systems arising in fluid mechanics and fluid dynamics.
Vikas Gupta, Mohan K. Kadalbajoo, and Ritesh K. Dubey
Informa UK Limited
ABSTRACT In the present paper, a parameter-uniform numerical method is constructed and analysed for solving one-dimensional singularly perturbed parabolic problems with two small parameters. The solution of this class of problems may exhibit exponential (or parabolic) boundary layers at both the left and right part of the lateral surface of the domain. A decomposition of the solution in its regular and singular parts has been used for the asymptotic analysis of the spatial derivatives. To approximate the solution, we consider the implicit Euler method for time stepping on a uniform mesh and a special hybrid monotone difference operator for spatial discretization on a specially designed piecewise uniform Shishkin mesh. The resulting scheme is shown to be first-order convergent in temporal direction and almost second-order convergent in spatial direction. We then improve the order of convergence in time by means of the Richardson extrapolation technique used in temporal variable only. The resulting scheme is proved to be uniformly convergent of order two in both the spatial and temporal variables. Numerical experiments support the theoretically proved higher order of convergence and show that the present scheme gives better accuracy and convergence compared of other existing methods in the literature.
Ritesh Kumar Dubey and Sabana Parvin
Springer Science and Business Media LLC
Ritesh Kumar Dubey and Biswarup Biswas
Elsevier BV