CDFIB: A convolutional direct forcing immersed boundary method for solving incompressible flows with time-varying geometries

Abstract

When incorporating the immersed boundary method to model solid obstacles in incompressible flows, the conventional direct forcing immersed boundary (DFIB) method may face the issue of spurious force oscillations (SFO) due to the mass imbalance when integrating drag/lift forces around the solid obstacle. Although the SFO can be controlled with large time step size when employing conventional DFIB method, the method remains prone to large SFO when the time step size is small. When we deal with flow-structure interaction (FSI) scenarios, the solid bodies are driven by hydrodynamic forces that are produced by flow fluids. Unphysical acceleration/deceleration may happen during the simulations due to SFO, thus making the simulations unstable or even diverge. To alleviate the SFO, we thus propose a novel method for modeling the solid bodies in incompressible fluid flows by performing the convolution kernel, dubbed as cDFIB method. cDFIB method inherits the merits of DFIB method, while effectively suppressing SFO for both small and large time step size. From the numerical results of the SFO oscillating cylinder problem, the SFO is proportional to O(Δx) and O(Δt) for present cDFIB method. This property allows cDFIB method to solve challenging problems where employing large time step size becomes infeasible.