Abstract
In the present work, a highly efficient incompressible flow solver with a semi-implicit time advancement on a fully staggered grid using a high-order compact difference scheme is developed firstly in the framework of approximate factorization. The fourth-order compact difference scheme is adopted for approximations of derivatives and interpolations in the incompressible Navier–Stokes equations. The pressure Poisson equation is efficiently solved by the fast Fourier transform (FFT). The framework of approximate factorization significantly simplifies the implementation of the semi-implicit time advancing with a high-order compact scheme. Benchmark tests demonstrate the high accuracy of the proposed numerical method. Secondly, by applying the proposed numerical method, we compute turbulent channel flows at low and moderate Reynolds numbers by direct numerical simulation (DNS) and large eddy simulation (LES). It is found that the predictions of turbulence statistics and especially energy spectra can be obviously improved by adopting the high-order scheme rather than the traditional second-order central difference scheme.
Highlights
The study of wall-bounded turbulent flows advanced a lot and benefited from high-fidelity numerical simulations [1,2,3], i.e., direct numerical simulation (DNS) and large eddy simulation (LES).The spectral method is the most popular for the simulation of wall-bounded turbulent flows like channel flow [4,5,6,7,8,9] and pipe flow [10,11,12,13] because of its inherently high accuracy
While the present interest is another type of scheme, i.e., the compact difference scheme [20], its advantage is the very compact stencil points to achieve high order, and we aim to study whether it can provide help in wall turbulence simulation
Crank–Nicolson scheme is implemented for the viscous terms, and we propose a new method in the framework of approximate factorization [54,55,56] to significantly simplify the implementation
Summary
The study of wall-bounded turbulent flows advanced a lot and benefited from high-fidelity numerical simulations [1,2,3], i.e., direct numerical simulation (DNS) and large eddy simulation (LES). The spectral method is the most popular for the simulation of wall-bounded turbulent flows like channel flow [4,5,6,7,8,9] and pipe flow [10,11,12,13] because of its inherently high accuracy. The finite difference (FD) and finite volume (FV) methods are much more flexible and have been widely used in practical applications, while mostly with second-order accuracy only. It is always a demanding task to design a numerical method to have both high-order accuracy and enough flexibility in complex geometry. It is noted that the second-order accurate central difference scheme on a staggered grid [14]
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