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Ritesh Kumar Dubey

Publications and source records attributed to Ritesh Kumar Dubey.

9 recordsLinked to original sources
arXiv2024

Entropy stable non-oscillatory fluxes: An optimized wedding of entropy conservative flux with non-oscillatory flux

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 ($F^s$). This novel approach paves a way to construct non-oscillatory entropy stable flux ($\hat{F}$) as a simple combination of $(F^*$ and $F^s)$ which inherently optimize the numerical diffusion in the entropy stable flux ($\hat{F}$) such that it reduces to the underlying non-oscillatory flux ($F^s$) in the flux sign stable region. This robust approach is (i) agnostic to the choice of flux pair $(F^*,F^s)$, (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 these entropy stable schemes completely remove spurious oscillations in approximating the discontinuities compared to the non-oscillatory schemes using underlying fluxes ($F^s$) only. Moreover, these entropy stable schemes maintain the formal order of accuracy of the lower order flux in the pair.

math.NA↗
arXiv2021

WENO interpolations and reconstructions using data bounded polynomial approximation

This work characterizes the structure of third and forth order WENO weights by deducing data bounded condition on third order polynomial approximations. Using these conditions, non-linear weights are defined for third and fourth order data bounded weighted essentially non-oscillatory (WENO) approximations. Computational results show that data bounded WENO approximations for smooth functions achieve required accuracy and do not exhibit overshoot or undershoot for functions with discontinuities and extrema. Further with suitable weights, high order data-bounded WENO approximations are proposed for WENO schemes.

math.NA↗
arXiv2019

Development of a new sixth order accurate compact scheme for two and three dimensional Helmholtz equation

In this work, a new compact sixth order accurate finite difference scheme for the two and three-dimensional Helmholtz equation is presented. The main significance of the proposed scheme is that its sixth order leading truncation error term does not explicitly depend on the associated wave number. This makes the scheme robust to work for the Helmholtz equation even with large wave numbers. The convergence analysis of the new scheme is given. Numerical results for various benchmark test problems are given to support the theoretical estimates. These numerical results confirm the accuracy and robustness of the proposed scheme.

math.NA↗
arXiv2019

A generalized framework to construct third order WENO weights using weight limiter functions

The main aim of this work is not to improve any existing non-linear weight but to give a generalized framework for the construction of non-linear weights to get non-oscillatory third order WENO schemes. It is done by imposing necessary conditions on weights to get non-oscillatory WENO reconstruction which give further insight on the structure of weights to ensure non-occurrence of oscillations and characterize the solution region for third order accuracy. This framework for WENO weights is new and completely different from the prevailing existing approach. New non-linear weights are designed using a function of smoothness parameter termed as weight limiter functions. Many such weight limiter functions are given and analyzed. These new weights are simple and by construction guarantee for exact third order accuracy in smooth solution region including smooth extrema away from critical point. Numerical results for various test problems are given and compared. Results show that proposed weights give third order accuracy without loosing the non-oscillatory shock capturing ability of the resulting scheme.

math.NA↗
arXiv2018

Accuracy Preserving ENO and WENO Schemes using Novel Smoothness Measurement

A novel procedure is given for choosing smoothest stencil to construct less oscillatory ENO schemes. The procedure is further used to define smoothness parameter in the non-linear weights of new WENO schemes. The main significant features of these new ENO and WENO schemes is that they are less oscillatory and achieve their relevant order of accuracy in the presence of critical points in the exact solution. It is shown theoretically as well as computationally in $L^1$ and $L^\infty$ norm. Moreover, computational results are given to show less oscillatory behavior of the new WENO scheme compared to WENO5-JS and WENO5-Z schemes.

math.NA↗
arXiv2015

Local principle satisfying high order total variation diminishing approximation for non-sonic data extrema

The main contribution of this work is to construct higher than second order accurate total variation diminishing (TVD) schemes which can preserve high accuracy at non-sonic extrema with out induced local oscillations. It is done in the framework of local maximum principle (LMP) and non-conservative formulation. The representative uniformly second order accurate schemes are converted in to their non-conservative form using the ratio of consecutive gradient. These resulting schemes are analyzed for their non-linear LMP/TVD stability bounds using the local maximum principle. Based on the bounds, second order accurate hybrid numerical schemes are constructed using a shock detector. Numerical results are presented to show that such hybrid schemes yield TVD approximation with second or higher order convergence rate for smooth solution with extrema.

math.NA↗
arXiv2015

On the stability of Forward in Time and Centred in Space (FTCS) scheme for scalar hyperbolic equation

It is well known that Forward Time and Centred in Space (FTCS) scheme for scalar Hyperbolic Conservation Law (HCL) is unconditionally unstable. The main contribution of this work to show that FTCS is conditionally stable for HCL. A new approach is used to give bounds on the initial data profile by transforming FTCS into two point convex combination scheme. Numerical results are given in support of the claim.

math.NA↗
arXiv2007

$J/ψ$ suppression in Au+Au collisions at RHIC : colour screening scenario in the bag model at variable participant numbers

We have modified the colour screening theory of Chu and Matsui by properly incorporating bag model equation of state for quark gluon plasma (QGP). We have also chosen the pressure parametrization rather than parametrizing energy density in the transverse plane. We assume that the QGP dense medium is expanding in the longitudinal direction obeying Bjorken boost invariant scaling law. Sequential melting of $χ_c$, $ψ^{'}$ and $J/ψ$ is also considered in this scenario. We have applied above formulation to the recent PHENIX experimental data of $J/ψ$ suppression in Au + Au collisions at RHIC. We find that the model gives a good description of data at mid-rapidity in terms of survival probability versus number of participants without any necessity of implementing (3+1)-dimensional expansion of the deconfined medium.

hep-ph↗