Efficiently high-order time-stepping R-GSAV schemes for the Navier–Stokes–Poisson–Nernst–Planck equations

Abstract

We propose in this paper two kinds of generalized scalar auxiliary variable (GSAV) approach with relaxation (R-GSAV) for the Navier–Stokes–Poisson–Nernst–Planck equations. By applying positive function transform approach for ion concentration equation, introducing auxiliary variable for energy equation and adopting consistent splitting approach for momentum equations, we construct fully decoupled, linearized and kth-order semi-implicit schemes. The proposed schemes have several advantages: the concentration components of the discrete solution preserve the properties of positivity and mass conservation; these are unconditionally energy stable; the corrected energy is consistent with the original energy; only require solving decoupled linear systems with constant coefficients at each time step. We present some numerical results to validate these schemes and investigate the dynamics with initial discontinuous concentrations.