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An incompressible Eulerian formulation for soft solids in fluids
| Content Provider | Semantic Scholar |
|---|---|
| Author | Jain, S. S. Mani, Ali |
| Copyright Year | 2017 |
| Abstract | Soft solids in fluids are ubiquitous in nature. Studies of these systems are of practical relevance in science and engineering. Some of the applications of this system involve the study of the interaction between micro-bubble collapse-induced shock waves with the tissue in an animal body, where the tissue can be modeled as a soft solid in blood, the study of the electroporation phenomenon, where the cell membrane can be modeled as a solid surrounded by fluid medium. A solid-fluid coupled system, also known as a fluid-structure interaction (FSI) problem, has historically been studied using a Lagrangian approach for the solid and an Eulerian approach for the fluid regions (see the, arbitrary Lagrangian-Eulerian approach of Hu et al. (2001)), but the method found success mostly in the stiff limit of the solids and was found to be too cumbersome for highly deforming solids. Efforts to couple fluids and solids on a single Eulerian grid have also been attempted, but with limited success. For example, the classical immersed boundary method (Peskin 1982), the cut-cell finite volume approach (Clarke et al. 1986) and the immersed interface method (LeVeque & Li 1994) all use a single Eulerian grid, but in most of these methods a deforming solid is considered as a boundary condition to solve for the fluid region, or a simple Hooke’s law (a spring model) is used to approximate the deformation of the the solids. Fully Eulerian approaches that can solve solids using true solid constitutive laws in solid regions coupled with fluid flow have been developed before but were limited to unbounded domains (see the, Eulerian Godunov method of Miller & Colella (2001)). A recent work by Kamrin et al. (2012) introduced the reference map technique (RMT), a fully Eulerian approach to the simulation of solids and an extension to FSI problems (Valkov et al. 2015). These authors simulated soft solids on a staggered grid in a compressible flow setting. We adopt the incompressible version of this formulation and assess various improvements to the original RMT method. Here, we present an accurate reference map technique (Jain & Mani 2017) for the simulation of incompressible soft solids in fluids. We discuss the improvements made in terms of the accuracy, cost, easy of implementation and robustness of the method and also discuss some of the best modeling practices. In what follows, we describe this improved formulation, adopting a heuristic approach. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://web.stanford.edu/~sjsuresh/jain2017.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
