Speaker: 朱文兴（香港中文大学（深圳））
Time: 14:00-15:00, Nov. 13 2024
Online: Zoom: 811 5638 1768（Password: msrc）
Venue: 至善楼602
Title: Structure preserving numerical schemes for the electrohydrodynamic models
Abstract:
Electrohydrodynamic(EHD) model plays an important role in the electric-convection phenomena. The basic governing equations of EHD are the Poisson-Nernst-Planck(PNP) equations for ionic motions and the Navier-Stokes equations for fluid motion. We aim to develop the efficient numerical algorithms preserving desirable physical structure properties, including mass conservation, free-energy dissipation by using the scalar auxiliary variable(SAV) technique.
Based on zero-energy-contribution feature, we consider the EHD model with variable electrical conductivity, we studied the effects of Coulombic force and power-law non-Newtonian fluid. Then, for EHD model with variable density and conductivity, we simulated the dispersion of electrical conductivity and the effect of electrical force on the Rayleigh-Taylor instability for both shear-thinning and shear-thicking fluid. The proposed energy schemes have been strictly proved the total energy dissipation.
Next, we consider ionic steric effects in EHD model. The logarithmic transformation for the concentration is used to preserve positivity property. A nonlocal auxiliary variable with respect to the free energy of Poisson-Nernst-Planck equations with steric effects and its associated ordinary differential equation are introduced. The obtained system is equivalent to the original system. A decoupled, second-order accurate in time and energy stable scheme with finite element approximations is presented. We simulated the free-energy dissipation and ionic steric effects.
For the diffusive Oldroyd-B viscoelastic EHD model describing the dynamics of complex viscoelastic fluids under the influence of electric fields, we presents decoupled numerical schemes. By introducing a nonlocal auxiliary variable involving the electric field energy and entropic contributions, we form a new system which is equivalent to the original equations. A logarithmic transformation is employed to maintain the positive definiteness of the conformation tensor and the positivity of ion concentrations. The numerical schemes are shown to be unconditionally energy stable and mass conservation. Moreover, the proposed schemes require only the solutions of linear systems and a algebric equation at each time step. Various numerical experiments are provided to verify the convergence rate and performance of the proposed scheme.
