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

Journal of Applied and Computational Mathematics Pub Date : 2018-01-01 DOI:10.4172/2168-9679.1000412

A. Rd, A. A., Rehman A, Qamar S

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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

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加权基本非振荡格式在尘-气流动模型中的应用

将加权非振荡(WENO)有限体积格式推广到尘埃-气体流动模型的数值近似。我们使用五阶WENO格式进行空间重建，并使用单调数值Lax-Friedrichs通量来逆风通量。采用三阶全变分递减(TVD)龙格-库塔算法，实现求解的及时推进。在低密度流动中，所提出的数值格式有效地处理了接触不连续，更有趣的是它保持了流动变量的正性。此外，所提出的数值格式显示激波和界面相互作用时没有伪振荡。考虑了几个一维黎曼问题，分析了所建议数值格式的精度。为了验证，我们将weno方案生成的解与众所周知的中心迎风方案生成的解以及粉尘-气体流动模型的解析解进行了比较。引用本文:Aslam RD, Ali A, Rehman A, Qamar S(2018)加权基本非振荡格式在尘-气流动模型中的应用。[J]计算机数学，7:412。doi: 10.4172 / 2168 - 9679.1000412

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Journal of Applied and Computational Mathematics

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