Decoupled, Positivity-Preserving and Unconditionally Energy Stable Schemes for the Electrohydrodynamic Flow with Variable Density

In this paper, we investigate the decoupled, positivity-preserving and unconditionally energy stable fully discrete finite element schemes for the electrohydrodynamic flow with variable density. After deriving some new features of the nonlinear coupled terms, by introducing scalar auxiliary variable methods to ensure the positivity and the boundedness of the approximation fluid density, we construct linear and decoupled first- and second-order fully discrete least square finite element methods for the model. Compared with the classical ones, not only the positivity-preserving technique in the proposed methods has the form invariance and is independent of the discrete methodology, but also much better computational cost and accuracy can be achieved. Moreover, by proposing modified zero-energy-contribution methods to balance the errors generated in the decoupled processes for the nonlinear coupled terms, we prove that two fully discrete schemes are unconditionally energy stable. The shown numerical examples confirm the superiority in the computational time, the positivity-preserving, the stability and the computational accuracy of the proposed schemes.