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For higher orders schemes, we observed super-convergence by one order for the scalar variable which is consistent with the previously published result for a symmetric diffusion tensor.
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High-order schemes are introduced.
Three ordering schemes of nodes are investigated.
The results suggest that high order schemes can be more computationally efficient than low order schemes.
We see that higher order schemes produce lower dissipation.
Higher order schemes are built using higher order moments.
Other higher order schemes can be constructed accordingly.
The second and fourth order schemes gave similar performance, while the fourth order scheme costs much more computationally.
The effects of the low Mach correction have more profound impact on second and third-order schemes, but they also improve the accuracy of fifth order schemes.
Lower order schemes suffer from excessive numerical diffusion, whereas higher order schemes suffer from dispersive ripples in the wake region of the flow.
It is obvious that the first-order schemes show no oscillation and good accuracy is obtained in the higher-order schemes.
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