Energetic variational approaches in modeling vesicle and fluid interactions

Du, Qiang; Li, Chun; Ryham, Rolf; Wang, Xiaoqiang

doi:10.1016/j.physd.2009.02.015

Cited by 82 publications

(122 citation statements)

References 37 publications

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“…• The high inertia (HI) flow given by (4.1) and (4.2) where the nondimensional parameters are taken to be Re = Be = 1 as in [19] where a phase field approach is advocated.…”

Section: Numerical Simulationsmentioning

confidence: 99%

See 1 more Smart Citation

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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Abstract. We derive a biomembrane model consisting of a fluid enclosed by a lipid membrane. The membrane is characterized by its Canham-Helfrich energy (Willmore energy with area constraint) and acts as a boundary force on the Navier-Stokes system modeling an incompressible fluid. We give a concise description of the model and of the associated numerical scheme. We provide numerical simulations with emphasis on the comparisons between different types of flow: the geometric model which does not take into account the bulk fluid and the biomembrane model for two different regimes of parameters.

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“…• The high inertia (HI) flow given by (4.1) and (4.2) where the nondimensional parameters are taken to be Re = Be = 1 as in [19] where a phase field approach is advocated.…”

Section: Numerical Simulationsmentioning

confidence: 99%

“…However, topological changes cannot be handled with the present method. We refer to the work of Du et al [19] for a phase-field method on a similar system.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of Biomembranes: Effect of the Bulk Fluid

Bonito

Nochetto

Pauletti

2011

Math. Model. Nat. Phenom.

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“…Then we apply a renormalization of the phase field by choosing n large in the weighting function p(t) = −2n(1 − t 2 ) n−1 t. Some formal asymptotic analysis is given to motivate the artificial relaxation scheme and its connection with the optimal profile used to derive (1.1) in section 2. We describe the relaxation scheme by an example from the general framework of an incompressible fluid/phase field coupling (see [9], for instance.) Let E = E(φ) ≥ 0 be an arbitrary energy functional and consider…”

Section: Relaxation and Renormalizationmentioning

confidence: 99%

Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization

Du¹,

Li²,

Ryham³

et al. 2007

Communications in Mathematical Sciences

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Abstract. We introduce a set of new interfacial energies for approximating the Euler number of level surfaces in the phase field (diffuse-interface) representation. These new formulae have simpler forms than those studied earlier in [Q. Du, C. Liu and X. Wang, Retrieving topological information for phase field models, SIAM J. Appl. Math., 65, 1913Math., 65, -1932Math., 65, , 2005, and do not contain higher order derivatives of the phase field function. Theoretical justifications are provided via formal asymptotic analysis, and practical validations are performed through numerical experiments. Relaxation and renormalization schemes are also developed to improve the robustness of the new energy functionals.

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“…The bilayer structure makes Vesicle Membranes simple models for studying the physico-chemical properties of cell as well as of their shape deformations. Many works related with this topic has been introduced in the literature is the last years, focusing on the derivation of models [17,18], establishment of analytical results of the systems [16,21,23] and their numerical approximations [19,22].…”

Section: Vesicle Membranesmentioning

confidence: 99%

“…In particular, we recall here the model derived in [17] to approximate the deformation of the fluid bound vesicle by means of an incompressible flow and phase field coupling. Indeed, this system can be viewed as a coupling between the Navier-Stokes equation with an Allen-Cahn system but where the energy related with the phase field function is the so-called bending energy and it is not the same energy considered in (1.1).…”

Section: Vesicle Membranesmentioning

confidence: 99%

Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models

Tierra

Guillén-González

2014

Arch Computat Methods Eng

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In this paper, we review some numerical methods presented in the literature in the last years to approximate the Cahn-Hilliard equation. Our aim is to compare the main properties of each one of the approaches to try to determine which one we should choose depending on which are the crucial aspects when we approximate the equations. Among the properties that we consider desirable to control are the time accuracy order, energy-stability, unique solvability and the linearity or nonlinearity of the resulting systems. In particular, we concern about the iterative methods used to approximate the nonlinear schemes and the constraints that may arise on the physical and computational parameters.Furthermore, we present the connections of the Cahn-Hilliard equation with other physically motivated systems (not only phase field models) and we state how the ideas of efficient numerical schemes in one topic could be extended to other frameworks in a natural way.

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Energetic variational approaches in modeling vesicle and fluid interactions

Cited by 82 publications

References 37 publications

Dynamics of Biomembranes: Effect of the Bulk Fluid

Dynamics of Biomembranes: Effect of the Bulk Fluid

Diffuse Interface Energies Capturing the Euler Number: Relaxation and Renomalization

Numerical Methods for Solving the Cahn–Hilliard Equation and Its Applicability to Related Energy-Based Models

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