TY - JOUR
T1 - Unconditional Bound-Preserving and Energy-Dissipating Finite-Volume Schemes for the Cahn-Hilliard Equation
AU - Bailo , Rafael
AU - Carrillo , José A.
AU - Kalliadasis , Serafim
AU - Perez , Sergio P.
JO - Communications in Computational Physics
VL - 3
SP - 713
EP - 748
PY - 2023
DA - 2023/10
SN - 34
DO - http://doi.org/10.4208/cicp.OA-2023-0049
UR - https://global-sci.org/intro/article_detail/cicp/22022.html
KW - Cahn-Hilliard equation, diffuse interface theory, gradient flow, finite-volume method, bound preservation, energy dissipation.
AB - <p style="text-align: justify;">We propose finite-volume schemes for the Cahn-Hilliard equation which
unconditionally and discretely preserve the boundedness of the phase field and the
dissipation of the free energy. Our numerical framework is applicable to a variety
of free-energy potentials, including Ginzburg-Landau and Flory-Huggins, to general
wetting boundary conditions, and to degenerate mobilities. Its central thrust is the upwind methodology, which we combine with a semi-implicit formulation for the free-energy terms based on the classical convex-splitting approach. The extension of the
schemes to an arbitrary number of dimensions is straightforward thanks to their dimensionally split nature, which allows to efficiently solve higher-dimensional problems with a simple parallelisation. The numerical schemes are validated and tested
through a variety of examples, in different dimensions, and with various contact angles
between droplets and substrates.</p>