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arXiv · 2305.19237

Stabilized immersed isogeometric analysis for the Navier-Stokes-Cahn-Hilliard equations, with applications to binary-fluid flow through porous media

Stein K. F. Stoter·Tom B. van Sluijs·Tristan H. B. Demont·E. Harald van Brummelen·Clemens V. Verhoosel
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Abstract

Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological changes of the binary-fluid interface. In this work, we propose an immersed isogeometric analysis framework to solve the Navier-Stokes-Cahn-Hilliard equations on domains with geometrically complex external binary-fluid boundaries. The use of optimal-regularity B-splines results in a computationally efficient higher-order method. The key features of the proposed framework are a generalized Navier-slip boundary condition for the tangential velocity components, Nitsche's method for the convective impermeability boundary condition, and skeleton- and ghost-penalties to guarantee stability. A binary-fluid Taylor-Couette flow is considered for benchmarking. Porous medium simulations demonstrate the ability of the immersed isogeometric analysis framework to model complex binary-fluid flow phenomena such as break-up and coalescence in complex geometries.

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Stein K. F. Stoter, Tom B. van Sluijs, Tristan H. B. Demont, E. Harald van Brummelen, Clemens V. Verhoosel. 2023-05-30. Stabilized immersed isogeometric analysis for the Navier-Stokes-Cahn-Hilliard equations, with applications to binary-fluid flow through porous media. https://arxiv.org/abs/2305.19237

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