A diffuse-interface approach for modelling transport, diffusion and adsorption/desorption of material quantities on a deformable interface. (English) Zbl 1186.35168

Teigen, Knut Erik; Li, Xiangrong; Lowengrub, John; Wang, Fan; Voigt, Axel

Commun. Math. Sci. 7, No. 4, 1009-1037 (2009); errata ibid. 10, No. 4, 1092 (2010).

Summary: A method is presented to solve two-phase problems involving a material quantity on an interface. The interface can be advected, stretched, and change topology, and material can be adsorbed to or desorbed from it. The method is based on the use of a diffuse interface framework, which allows a simple implementation using standard finite-difference or finite-element techniques. Here, finite-difference methods on a block-structured adaptive grid are used, and the resulting equations are solved using a non-linear multigrid method. Interfacial flow with soluble surfactants is used as an example of the application of the method, and several test cases are presented demonstrating its accuracy and convergence.

MSC:

35Q35	PDEs in connection with fluid mechanics
76T10	Liquid-gas two-phase flows, bubbly flows
76M20	Finite difference methods applied to problems in fluid mechanics
82C24	Interface problems; diffusion-limited aggregation in time-dependent statistical mechanics
76R50	Diffusion
65M55	Multigrid methods; domain decomposition for initial value and initial-boundary value problems involving PDEs
65M50	Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Keywords:

partial differential equations; diffuse interface; interfacial dynamics; complex geometry; multigrid; adaptive grid; finite difference; multiphase; adsorption; desorption