Physics of Fluids - Publications

A robust and accurate adaptive approximation method for a diffuse-interface model of binary-fluid flows

Open Access
Computer Methods in Applied Mechanics and Engineering 400, 115563 (2022)

Authors

	T.H.B. Demont
	G.J. van Zwieten
	Christian Diddens
	Harald van Brummelen

BibTeΧ

@article{DEMONT2022115563,
title = {A robust and accurate adaptive approximation method for a diffuse-interface model of binary-fluid flows},
journal = {Computer Methods in Applied Mechanics and Engineering},
volume = {400},
pages = {115563},
year = {2022},
issn = {0045-7825},
doi = {https://doi.org/10.1016/j.cma.2022.115563},
url = {https://www.sciencedirect.com/science/article/pii/S004578252200545X},
author = {T.H.B. Demont and G.J. {van Zwieten} and C. Diddens and E.H. {van Brummelen}},
keywords = {Navier‚ÄìStokes‚ÄìCahn‚ÄìHilliard equations, Diffuse-interface models, Binary-fluid flows, Adaptive refinement, -continuation, Partitioned solution methods},
abstract = {We present an adaptive simulation framework for binary-fluid flows, based on the Abels‚ÄìGarcke‚ÄìGr√ºn Navier‚ÄìStokes‚ÄìCahn‚ÄìHilliard (AGG NSCH) diffuse-interface model. The adaptive-refinement procedure is guided by a two-level hierarchical a-posteriori error estimate, and it effectively resolves the spatial multiscale behavior of the diffuse-interface model. To improve the robustness of the solution procedure and avoid severe time-step restrictions for small-interface thicknesses, we introduce an …õ-continuation procedure, in which the diffuse interface thickness (…õ) are enlarged on coarse meshes, and the mobility is scaled accordingly. To further accelerate the computations and improve robustness, we apply a modified Backward Euler scheme in the initial stages of the adaptive-refinement procedure in each time step, and a Crank‚ÄìNicolson scheme in the final stages of the refinement procedure. To enhance the robustness of the nonlinear solution procedure, we introduce a partitioned solution procedure for the linear tangent problems in Newton‚Äôs method, based on a decomposition of the NSCH system into its NS and CH subsystems. We conduct a systematic investigation of the conditioning of the monolithic NSCH tangent matrix and of its NS and CH subsystems for a representative 2D model problem. To illustrate the properties of the presented adaptive simulation framework, we present numerical results for a 2D oscillating water droplet suspended in air, and we validate the obtained results versus those of a corresponding sharp-interface model.}
}