Large-eddy simulation of convective boundary layer using explicit difference schemes

A new numerical approach to the time integration of a large-eddy simulation model of the atmospheric convective boundary layer is presented. To solve the Cauchy problem for the set of ordinary differential equations, dY/dt = F(Y), which results from the finite-difference approximation of the original problem, the stable explicit scheme with time-varying steps is used. This method is based on the combination of Euler schemes and the properties of the roots of the Chebyshev polynomials. It is found that using a priori information about the smoothness of the solution and the spectrum of the Jacobian, dF/dY, and prescribing the order of accuracy of local approximation, the algorithm proposed allows us to perform timesteps quite efficiently and obtain a significant gain in the total computation time as compared with the three-layer leap-frog scheme. The results of some numerical experiments are also presented and briefly discussed.