Application of Weighted Essentially Non-Oscillatory Scheme to Solve the Dusty-Gas Flow Model

Abstract

A weighted essentially non-oscillatory (WENO) finite volume scheme is extended to approximate the model of dusty-gas flow numerically. We use a WENO scheme of the fifth-order for the spatial reconstruction and a monotone numerical Lax-Friedrichs flux to upwind the fluxes. A 3rd-order total variation diminishing (TVD) Runge-Kutta algorithm is to be utilized to march the solution in time. In low density flows, the proposed numerical scheme effectively handles the contact discontinuities and more interestingly it sustains the positivity of flow variables. Furthermore, the proposed numerical scheme shows no spurious oscillations where shock waves and interfaces interact. Several one-dimensional Riemann problems are considered to analyse the accuracy of suggested numerical scheme. For validation, we compare the solutions generated by WENO-scheme with the solutions generated by well known central-upwind scheme and analytical solutions available for the model of dusty-gas flow. Citation: Aslam RD, Ali A, Rehman A, Qamar S (2018) Application of Weighted Essentially Non-Oscillatory Scheme to Solve the Dusty-Gas Flow Model. J Appl Computat Math 7: 412. doi: 10.4172/2168-9679.1000412