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A third-order shock capturing scheme for inviscid flows

Mohamad, Mahmod Abd Hakim and Abd Aziz, Azizul Rahman and Mohamed Nor, Mohd Hadri and Basuno, Bambang (2013) A third-order shock capturing scheme for inviscid flows. In: Prosiding Seminar Kebangsaan Aplikasi Sains dan Matematik 2013 (SKASM 2013) , 29-30 Oktober 2013, Batu Pahat, Johor . (Unpublished)

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Abstract

In this paper, a third-order compact upwind scheme is specified for calculating flows containing discontinuities. A detailed investigation was conducted to assess the performance of the basic third-order compact central discretization schemes. From observation, discretization of the convective flux terms of the Euler equation is based on a hybrid flux-vector splitting, known as the advection upstream splitting method (AUSM) scheme which combines the accuracy of flux-difference splitting and the robustness of flux-vector splitting. The scheme utilizes the AUSM flux splitting method and a third-order compact upwind space discretization relation for calculating third-order numerical flux function. The idea of total variation diminishing (TVD), by limiting the flux gradient, is used to capture discontinuities. TVD shock capturing properties of the scheme are achieved through a minmod flux limiter. A multistage TVD Runge-Kutta method is employed for the time integration. In addition to that, development and modification of source code for the one-dimensional flow is validated with two test cases namely, unsteady shock tube and quasi-onedimensional- supersonic-subsonic flow. Further analysis had also been done in comparing the characteristic of AUSM scheme against experimental results, obtained from previous works and comparative analysis with computational results generated by van Leer and KFVS schemes. Furthermore, there is a remarkable improvement with the extension of the third-order AUSM scheme, the improvement of shock capturing properties such as the accuracy of shocks, contact discontinuities and rarefaction waves were achieved.

Item Type: Conference or Workshop Item (Paper)
Uncontrolled Keywords: third-order; upwind scheme; AUSM; TVD; Runge-Kutta
Subjects: T Technology > TA Engineering (General). Civil engineering (General) > TA349-359 Mechanics of engineering. Applied mechanics
Divisions: Centre of Diploma Studies > Department of Mechanical Engineering
Depositing User: Normajihan Abd. Rahman
Date Deposited: 29 Jun 2015 06:49
Last Modified: 29 Jun 2015 06:49
URI: http://eprints.uthm.edu.my/id/eprint/4514
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