| Abstract: |
| We consider in this paper gradient flows with disparate terms in the free energy that can not be efficiently handled with the scalar auxiliary variable (SAV) approach, and develop
the multiple scalar auxiliary variable (MSAV) approach to deal with these cases. We apply the MSAV approach to the phase-field vesicle membrane (PF-VMEM) model which, in addition to some usual nonlinear terms in the free energy, has two additional penalty terms to enforce the volume and surface area.
The MSAV approach enjoys the same computationally advantages as the SAV approach, but can handle free energies with multiple disparate terms such as the volume and surface area constraints in the PF-VMEM model.
The MSAV schemes are
unconditional energy stable, second-order accurate in time, and
can be decoupled, at each time step, into three linear fourth-order equations with constant coefficients, each can be further reduced to two Poisson type equations. Hence, these schemes are easy to implement and extremely efficient when coupled with an adaptive time stepping.
Ample numerical results are presented to validate the stability and accuracy of the MSAV schemes. |
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