Kavli Affiliate: Ke Wang
| First 5 Authors: Meng Li, Ke Wang, Nan Wang, ,
| Summary:
A multitude of substances exist as mixtures comprising multiple chemical
components in the natural world. These substances undergo morphological changes
under external influences. the phase field model coupled with fluid flow, the
dynamic movement and evolution of the phase interface intricately interact with
the fluid motion. This article focuses on the N-component models that couple
the conservative Allen-Cahn equation with two types of incompressible fluid
flow systems: the Navier-Stokes equation and the Darcy equation. By utilizing
the scalar auxiliary variable method and the projection method, we innovatively
construct two types of structure-preserving weighted implicit-explicit schemes
for the coupled models, resulting in fully decoupled linear systems and
second-order accuracy in time. The schemes are proved to be mass-conservative.
In addition, with the application of $G$-norm inspired by the idea of
$G$-stability, we rigorously establish its unconditional energy stability.
Finally, the performance of the proposed scheme is verified by some numerical
simulations.
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