Immersed boundary simulations of flows driven by moving thin membranes

Immersed boundary methods are extensively used for simulations of dynamic solid objects interacting with fluids due to their computational efficiency and modelling flexibility compared body-fitted grid methods. However, thin geometries, such as shells membranes, cause a violation the conditions across surface many immersed projection algorithms. Using one-dimensional analytical derivation multi-dimensional numerical simulations, this manuscript shows that adjustment Poisson matrix itself is require avoid large velocity, pressure, force prediction errors when pressure jump interface substantial these increase Reynolds number. A new minimal thickness modification developed Boundary Data Immersion Method (BDIM-{\sigma}),which avoids issues while still enabling use efficient algorithms high-speed simulations.