Multiscale Analysis and Numerical Simulations for Stability of Incompressible Periodic Flow of Maxwell Fluid

摘要

For incompressible small-scale flow of Maxwell fluid subject to forcing periodic in space and time, the mean-field equations were obtained by the multiscale asymptotic analysis. A general mathematical formalism was developed to determine the effective tensor. The mean-field equations were derived in detail and the exact explicit expressions of the effective tensor were given for the parallel time-independent flow. For Kolmogorov flow, the critical value of viscosity for stability of the large scale perturbations was obtained by a theoretic analysis of eigenvalues of the homogenized operator in the mean-field equations. And then the original linearized equations were simulated directly by using SIMPLEC algorithm in the collocated grid system. The comparisons between the results of direct numerical simulations and the theoretic predictions of multiscale analysis demonstrate the multiscale asymptotic analysis and the numerical algorithm used in this paper are effective and credible.