Multiscale Analysis and Numerical Simulations for Stability of Incompressible Flow of Maxwell Fluid
Zhang Hong-ping · Gongcheng shuxue xuebao · 2009
For the incompressible small-scale periodic flow of a Maxwell fluid, the mean-field equations which govern the transport of large-scale perturbations were obtained by the multiscale analysis. A general mathematical formalism was developed to determine the effective tensor. In general, the effective tensor is a fourth-order tensor, for which a compact representation was provided. The exact explicit expressions of the effective tensor were given for the parallel time-independent flow. For the Kolmogorov flow, the critical value of viscosity for stabilities of large scale perturbations was obtained by theoretical analyses of the eigenvalues of the homogenized operator in the mean-field equations. Then, the mean-field equations and the original linearized equations with respect to different parameters and initial conditions were simulated by using the modified SIMPLEC (Semi-Implicit Method for Pressure Linked Equations, Consistent) algorithm in the collocated grid system. The comparisons between the direct numerical simulations and the multiscale theoretic predictions demonstrated that the multiscale analysis and the numerical algorithm are effective and credible.