We have recently developed a novel numerical method for fluid–solid and fluid–membrane interaction problems. The method is based on a finite difference fractional step technique, corresponding to a standard numerical approach for simulating incompressible fluid flows, and applicable to treating nonlinear constitutive laws of solid/membrane and large deformations. The temporal change of the solid deformation is described in the Eulerian frame by updating the advection equations for a left Cauchy-Green deformation tensor, which is used to express the constitutive equations for materials and membranes. This method is reviewed in detail with some numerical results.
A Review of Full Eulerian Methods for Fluid Structure Interaction Problems
Takagi, S., Sugiyama, K., Ii, S., and Matsumoto, Y. (December 13, 2011). "A Review of Full Eulerian Methods for Fluid Structure Interaction Problems." ASME. J. Appl. Mech. January 2012; 79(1): 010911. https://doi.org/10.1115/1.4005184
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