Abstract
In this work, we have proposed two new combined compact difference (CCD) schemes for the solution of Navier---Stokes equations. These spatial discretization schemes have not only high spectral resolution for obtaining first and second derivative terms, but also have improved dispersion relation preserving properties when the fourth-order four-stage Runge---Kutta scheme is used for time integration. Out of the two proposed CCD schemes, the first scheme has upwind stencil, while the second scheme has a central stencil. Important numerical properties of these schemes have been analyzed and their effectiveness have been shown by solving the model wave equations, as well as Navier---Stokes equations. Results show that the upwind CCD scheme is suitable for high accuracy large eddy simulation of transitional and turbulent flowfields.
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