A three-dimensional immersed boundary method for non-Newtonian fluids

Fluid-structure-interaction (FSI) phenomenon is common in science and engineering. The fluid involved in an FSI problem may be non-Newtonian such as blood. A popular framework for FSI problems is Peskin's immersed boundary (IB) method. However, most of the IB formulations are based on Newtonian fluids. In this letter, we report an extension of the IB framework to FSI involving Oldroyd-B and FENE-P fluids in three dimensions using the lattice Boltzmann approach. The new method is tested on two FSI model problems. Numerical experiments show that the method is conditionally stable and convergent with the first order of accuracy.