A ghost cell immersed boundary method coupled with Aitken Schwarz DDM for computation of Liquid-Liquid Phase Fronts on Fixed Grids

摘要

Problems with moving interfaces are usual in computational fluid dynamics for different domains of applications such as fluid-structure interaction problems, frontal polymerization problems, hemodynamics problems, sea pollution by oiled problems... . This paper will detail the first steps to build a computational library that can handle such problems with a module oriented approach that domain decomposition and code coupling provide. Since the targeted computing architecture will be the grid, we focus on domain decomposition numerical methods that are tolerant to low bandwidth and high latencies as the Aitken-Schwarz method developed in [3] and that performs well in metacomputing framework as shown in [1] with a 5 Mbit/s ethernet network. First we concentrate on the space discretization associated with the domain decomposition generated by the moving interface. The numerical solution of flow for fluids separated by a moving interface, in order to track liquid-liquid boundaries on a fixed underlying grid constitutes our first test problem to define the methodologies. Our approach consists to combine two numerical techniques to handle the interface movement. First, following a methodology proposed by Udaykumar & al.[5], the interface tracking where the interface is not considered to be of finite thickness but is treated as a discontinuity and is explicitly tracked. Second the Ghost Cell Immersed Boundary Method (IBM) of Tseng & Ferziger where the boundary conditions on a sharp interface is taken in account exactly through some ghost cells nodes in the vicinity of the interface, leading to a coefficient stencil readjustment. This approach seems for us to fit the grid computing architecture as only the knowledge of the interface position is needed. The load balancing consideration of structured mesh is for us more reachable than re-meshing techniques.