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

T.H.B. Demont; G.J. van Zwieten; C. Diddens; E.H. van Brummelen

doi:10.1016/j.cma.2022.115563

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

T.H.B. Demont (Corresponding author), G.J. van Zwieten, C. Diddens, E.H. van Brummelen

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Abstract

We present an adaptive simulation framework for binary-fluid flows, based on the Abels–Garcke–Grün Navier–Stokes–Cahn–Hilliard (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 ɛ-continuation procedure, in which the diffuse interface thickness (ɛ) 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–Nicolson 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's 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.

Original language	English
Article number	115563
Number of pages	35
Journal	Computer Methods in Applied Mechanics and Engineering
Volume	400
DOIs	https://doi.org/10.1016/j.cma.2022.115563
Publication status	Published - 1 Oct 2022

Funding

This research was partly conducted within the Industrial Partnership Program Fundamental Fluid Dynamics Challenges in Inkjet Printing (FIP), a joint research program of Canon Production Printing, Eindhoven University of Technology, University of Twente, and the Netherlands Organization for Scientific Research (NWO). T.H.B. Demont and C. Diddens gratefully acknowledge financial support through the FIP program . All simulations have been performed using the open source software package Nutils [47] ( www.nutils.org ).

Keywords

Adaptive refinement
Binary-fluid flows
Diffuse-interface models
Navier–Stokes–Cahn–Hilliard equations
Partitioned solution methods
ɛ-continuation

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

abstract = "We present an adaptive simulation framework for binary-fluid flows, based on the Abels–Garcke–Gr{\"u}n Navier–Stokes–Cahn–Hilliard (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 ɛ-continuation procedure, in which the diffuse interface thickness (ɛ) 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–Nicolson 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's 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.",

keywords = "Adaptive refinement, Binary-fluid flows, Diffuse-interface models, Navier–Stokes–Cahn–Hilliard equations, Partitioned solution methods, ɛ-continuation",

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note = "Funding Information: This research was partly conducted within the Industrial Partnership Program Fundamental Fluid Dynamics Challenges in Inkjet Printing (FIP), a joint research program of Canon Production Printing, Eindhoven University of Technology, University of Twente, and the Netherlands Organization for Scientific Research (NWO). T.H.B. Demont and C. Diddens gratefully acknowledge financial support through the FIP program . All simulations have been performed using the open source software package Nutils [47] ( www.nutils.org ). Publisher Copyright: {\textcopyright} 2022 The Authors",

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AU - Demont, T.H.B.

AU - van Zwieten, G.J.

AU - Diddens, C.

AU - van Brummelen, E.H.

N1 - Funding Information: This research was partly conducted within the Industrial Partnership Program Fundamental Fluid Dynamics Challenges in Inkjet Printing (FIP), a joint research program of Canon Production Printing, Eindhoven University of Technology, University of Twente, and the Netherlands Organization for Scientific Research (NWO). T.H.B. Demont and C. Diddens gratefully acknowledge financial support through the FIP program . All simulations have been performed using the open source software package Nutils [47] ( www.nutils.org ). Publisher Copyright: © 2022 The Authors

PY - 2022/10/1

Y1 - 2022/10/1

N2 - We present an adaptive simulation framework for binary-fluid flows, based on the Abels–Garcke–Grün Navier–Stokes–Cahn–Hilliard (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 ɛ-continuation procedure, in which the diffuse interface thickness (ɛ) 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–Nicolson 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's 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.

AB - We present an adaptive simulation framework for binary-fluid flows, based on the Abels–Garcke–Grün Navier–Stokes–Cahn–Hilliard (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 ɛ-continuation procedure, in which the diffuse interface thickness (ɛ) 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–Nicolson 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's 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.

KW - Adaptive refinement

KW - Binary-fluid flows

KW - Diffuse-interface models

KW - Navier–Stokes–Cahn–Hilliard equations

KW - Partitioned solution methods

KW - ɛ-continuation

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DO - 10.1016/j.cma.2022.115563

M3 - Article

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SN - 0045-7825

VL - 400

JO - Computer Methods in Applied Mechanics and Engineering

JF - Computer Methods in Applied Mechanics and Engineering

M1 - 115563

ER -

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

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