Propagation of diffusing pollutant by kinetic flux-vector splitting method

In this article, the transport of a passive pollutant by a flow modeled by shallow water equations is numerically investigated. The kinetic flux-vector splitting (KFVS) scheme is extended to solve the one and two-dimensional equations. The first two equations of the considered model are mass and momentum equations and the third equation is the transport equation. The suggested scheme focuses on the direct splitting of the macroscopic flux functions at the cell interfaces. It achieves second-order accuracy by using MUSCL-type initial reconstruction and the Runge–Kutta time stepping technique. Several numerical test problems from literature are considered to check the efficiency and performance of the scheme. The results of the proposed scheme are compared to the central scheme for validation. It is found that the results of both the schemes are in close agreement with each other. However, our suggested KFVS scheme resolves the sharp discontinuous profiles precisely.

Household Cooking Fuel Patterns in Rural India: Pre- and Post-Pradhan Mantri Ujjwala Yojana

This article analyses the performance and limitations of the Pradhan Mantri Ujjwala Yojana (PMUY), a central scheme launched in the year 2016 for the provision of liquefied petroleum gas (LPG) connections to Below Poverty Line households in the country. It shows that the scheme offered more than 80 million LPG connections and contributed to a sharp replacement of traditional fuel (firewood, kerosene, dung cake, etc.) between the years 2014 and 2018. However, a large share of these new consumers appears to have stopped LPG consumption soon after the distribution under the scheme. This is clearly evident in the huge number of inactive LPG connections which continue to increase—from 35.8 million inactive connections in the country in 2017 to 43.2 million in 2019. Though PMUY contributed to the increase in LPG connections, it failed to accelerate its consumption demand among the beneficiaries. Nearly ₹128 billion has been spent by the government in form of subsidies and around 70% of the PMUY beneficiaries have availed loans from Oil Manufacturing Companies (OMCs). If the LPG consumption fails to accelerate, these one-time subsidies provided by the government will fail to achieve the objective and the loans disbursed by the OMCs may turn into non-performing assets.

A stiffly stable semi-discrete scheme for the characteristic linear hyperbolic relaxation with boundary

We study the stability of the semi-discrete central scheme for the linear damped wave equation with boundary. We exhibit a sufficient condition on the boundary to guarantee the uniform stability of the initial boundary value problem for the relaxation system independently of the stiffness of the source term and of the space step. The boundary is approximated using a summation-by-parts method and the stiff stability is proved using energy estimates and the Laplace transform. We also investigate if the condition is also necessary, following the continuous case studied by Xin and Xu (J. Differ. Equ. 167 (2000) 388–437).

Analysis of Two Finite Dierence Schemes for a Channel Flow Problem

Aims/ Objectives: To investigate the influence of a model parameter on the convergence of two finite difference schemes designed for a convection-diffusion-reaction equation governing the pressure-driven flow of a Newtonian fluid in a rectangular channel.Methodology: By assuming a uni-directional and incompressible channel flow with an exponentially time-varying suction velocity, we formulate a variable-coefficient convectiondiffusion- reaction problem. In the spirit of the method of manufactured solutions, we first obtain a benchmark analytic solution via perturbation technique. This leads to a modified problem which is exactly satisfied by the benchmark solution. Then, we formulate central and backward difference schemes for the modified problem. Consistency and convergence results are obtained in detail. We show, theoretically, that the central scheme is convergent only for values of a model parameter up to an upper bound, while the backward scheme remains convergent for all values of the parameter. An estimate of this upper bound, as a function of the mesh size, is derived. We then conducted numerical experiments to verify the theoretical results.Results: Numerical results showed that no numerical oscillations were observed for values of the model parameter less than the theoretically derived bound.Conclusion: We therefore conclude that the theoretical bound is a safe value to guarantee non-oscillatory solutions of the central scheme.

Investigation of Slotted Tip Parameters on the Aerodynamic Characteristic of Helicopter Rotor

Numerical simulations are conducted to investigate the effect of helicopter rotor tip vortex alleviation using a slotted tip, and effects of parameters involving location, number, aperture of the slot on tip vortex structure and aerodynamic performance are analyzed in detail. The flow field of hovering helicopter rotor is simulated by solving Navier-Stokes equations in the rotating coordinate system. Finite volume method combined with overset unstructured grids algorithm are adopted. The calculation of inviscid fluxes uses second-order central scheme with artificial dissipation, and turbulence model utilizes Spalart-Allmaras model. Simulation results show that the location of the slot has little effect on tip vortex alleviation. The larger the number and aperture of the slot, the better the effect of slotted tips weakening tip vortex. Lift coefficient of helicopter rotor with a slotted tip increases slightly compared with that without slots, while power coefficient increases drastically.