| Abstract: |
| A vesicle is a liquid droplet with a radius of about $10 \mu m$ enclosed by a phospholipid membrane suspended in an incompressible viscous fluid. The understanding of vesicle behaviors in fluid flows might lead to a better knowledge of red blood cells (RBCs). The dynamics of vesicle in fluids can be determined by the membrane inextensibility, bending, and hydrodynamical forces. There are two different approaches to enforce the local inextensibility constraint in literature. The first one needs to discretize the whole equations first and then to solve the discretized equations simultaneously for the tension and fluid variables. There usually exists a trade-off between the time-step stability and efficiency in those algorithms simply because iterative procedures are needed. Another approach is called a penalty idea. Instead of keeping the vesicle membrane locally inextensible, the penalty idea makes the vesicle surface patch nearly inextensible by introducing a modified elastic tension energy. This approach replaces the unknown tension by a spring-like tension depending on the surface configuration so that we can avoid solving the whole system to obtain the variable tension. In this talk, we present the extension of our previous immersed boundary method for simulating inextensible vesicles to general three dimensions. |
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