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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.
Other higher order schemes can be constructed accordingly.
Higher order schemes are built using higher order moments.
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.
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High-order schemes are introduced.
It is obvious that the first-order schemes show no oscillation and good accuracy is obtained in the higher-order schemes.
These oscillations are generated already by first-order schemes, but become more pronounced in higher-order schemes due to their lower dissipation.
Vertical advection is implicitly embedded in the remapping step and directly benefits from high-order schemes.
This chapter focuses on arbitrary-order schemes for parallel computational fluid dynamics (CFD) calculations.
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