A third-order shock capturing scheme for inviscid flows

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...

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Bibliographic Details
Main Authors: Mohamad, Mahmod Abd Hakim, Abd Aziz, Azizul Rahman, Mohamed Nor, Mohd Hadri, Basuno, Bambang
Format: Conference or Workshop Item
Published: 2013
Subjects:
Online Access:http://eprints.uthm.edu.my/4514/
http://eprints.uthm.edu.my/4514/1/A_THIRD%2DORDER_SHOCK_CAPTURING_SCHEME.pdf
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Summary: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.