A sharp-interface Cartesian grid method for viscoelastic fluid flow in complex geometry

Computational method on Cartesian mesh is popular in simulating fluid flow with moving boundaries of complex geometry. In this paper, a sharp-interface Cartesian grid method is proposed for the simulation of viscoelastic fluid flow. We implement a finite volume numerical scheme with an improved Rhie-Chow interpolation on the open-source platform OpenFOAM. The order of accuracy in space is shown to be second-order for Newtonian fluid flow and first-order for Oldroyd-B fluid flow. The correctness of our code is validated with the benchmark case of flow past a cylinder. The new sharp-interface Cartesian grid method is verified to correctly predict the viscoelastic stress on the surface of the cylinder. Simulation results of confined Oldroyd-B fluid flow past a pair of cylinders are also reported. A comparison between the proposed sharp-interface Cartesian grid method and a smoothed-interface immersed boundary method is carried out in terms of accuracy and efficiency at the end of this study.