Totally decoupled implicit–explicit linear scheme with corrected energy dissipation law for the phase-field fluid vesicle model

A biological vesicle in fluid environment is described by a conservative Allen–Cahn type phase-field model and the incompressible Navier–Stokes equations. To accurately and efficiently solve this complex system, we present a totally decoupled, linear, and second-order time-accurate method based on a time-dependent auxiliary variable methodology. The time-discretized versions of energy stability and unique solvability are analytically proved. By using a simple and effective energy correction technique, the consistency between the original and modified energies is enhanced. The proposed numerical algorithm is simple to implement because we only need to separately solve linear elliptic equations. Various computational tests are conducted to verify the performance of the proposed numerical algorithm.