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.

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