Positive-definiteness Preserving and Energy Stable Time-Marching Scheme for a Diffusive Oldroyd-B Electrohydrodynamic Model

In this paper, we develop a new time-marching scheme for a viscoelastic electrohydrodynamic model that satisfies an energy dissipation law. The scheme is based on the logarithmic conformation formulation so that it naturally preserves the positive-definiteness of the conformation tensor. The backward Euler scheme with the semi-Lagrangian formulation is used to construct the time-stepping scheme, with finite difference method on staggered grid for spatial discretization. The scheme is proved to be unconditionally energy stable at the fully discrete level and a fixed-point iteration is designed for its efficient implementation. Numerical experiments are given to verify the convergence rates and the energy stability of the scheme. Finally, the flow structure within the electro-convection phenomena has been studied in detail, focusing on an understanding of the elastic effect of fluids. (C) 2020 Elsevier B.V. All rights reserved.