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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| Main Authors: | , , , |
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| Format: | Conference or Workshop Item |
| Published: |
2013
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| 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. |
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