A non-iterative direct forcing immersed boundary method for strongly-coupled fluid-solid interactions

A non-iterative direct forcing immersed boundary method is presented for the strongly-coupled simulations of fluid-solid interactions. While it retains many advantages of the immersed boundary framework by Yang and Stern (2012) [30], especially the simplified field extension strategy for moving boundary treatment and the pointwise integration of hydrodynamic force using the momentum forcing term, the present approach improves upon the previous method in several aspects including optimized computational cost for a strong coupling scheme, reduced algorithm complexity for a straightforward implementation, and enhanced numerical stability for low density ratio problems. Central to these improvements is a simple intermediate step in which the velocity fields around solid bodies are predicted on temporary non-inertial reference frames attached to moving solid bodies in a one-to-one manner. This step enables the explicit inverse of the implicit equations for rigid body dynamics, thus rendering unnecessary the previous predictor-corrector scheme for iteratively adjusting the displacements and velocities of the immersed bodies until reaching a convergence. In addition, a simple, generalized procedure is developed to obtain the interpolation coefficients in a local reconstruction stencil explicitly from the geometric relationship. For verification and validation, the vortex-induced vibration of a circular cylinder and the rotational galloping of a rectangular body are considered first; then several particulate flow problems, including settling and buoyant particles of low density ratios, a settling particle in a small container, and the kissing-drafting-tumbling problem of two settling particles, are studied. The agreement between the present results and the reference data in the literature is excellent. An overall second-order accuracy of the algorithm is verified in two systematic grid convergence tests. The present idea can be easily applied to similar methods for achieving a strong coupling scheme on top of a weak one with a nominal increase in the computational cost. Details of the algorithm are provided to facilitate its implementation in other solvers using non-boundary-conforming grids.