One-dimensional high-order compact method for solving Euler’s equations
In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid, compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type schemes. Previously, this system was developed through computational...
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| Main Authors: | , , |
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| Format: | Conference or Workshop Item |
| Published: |
2011
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| Subjects: | |
| Online Access: | http://eprints.uthm.edu.my/2172/ http://eprints.uthm.edu.my/2172/1/Hakim_PPD_(IMAT2011).pdf |
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| Summary: | In the field of computational fluid dynamics, many numerical algorithms have been developed to simulate inviscid,
compressible flows problems. Among those most famous and relevant are based on flux vector splitting and Godunov-type
schemes. Previously, this system was developed through computational studies by Mawlood [1]. However the new test cases for
compressible flows, the shock tube problems namely the receding flow and shock waves were not investigated before by
Mawlood [1]. Thus, the objective of this study is to develop a high-order compact (HOC) finite difference solver for onedimensional
Euler equation. Before developing the solver, a detailed investigation was conducted to assess the performance of the
basic third-order compact central discretization schemes. Spatial discretization of the Euler equation is based on flux-vector
splitting. From this 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 AUSM scheme is based on the third-order compact scheme to the
approximate finite difference equation was completely analyzed consequently. In one-dimensional problem for the first order
schemes, an explicit method is adopted by using time integration method. In addition to that, development and modification of
source code for the one-dimensional flow is validated with four test cases namely, unsteady shock tube, quasi-one-dimensional
supersonic-subsonic nozzle flow, receding flow and shock waves in shock tubes. From these results, it was also carried out to
ensure that the definition of Riemann problem can be identified. Further analysis had also been done in comparing the
characteristic of AUSM scheme against experimental results, obtained from previous works and also comparative analysis with
computational results generated by van Leer, KFVS and AUSMPW schemes. Furthermore, there is a remarkable improvement
with the extension of the AUSM scheme from first-order to third-order accuracy in terms of shocks, contact discontinuities and
rarefaction waves. |
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