A sub-cell spectral-element simulator for 2D rigid-body-fluid interaction problems

In this work, we propose an immersed-boundary-type simulation method for the two-way coupling problems between a rigid body and a fluid. In this simulation tool, the entire fluid-solid domain is treated as an incompressible fluid with non-uniform density and the no-slip boundary condition at the rigid body surface is enforced by the penalization method. The fluid solver is developed in use of the spectral element method for the spatial discretization and the mixed explicit/implicit scheme for the temporal discretization. An additional Lagrangian mesh is employed and attached to the rigid body in order to trace the rigid body and to perform the area integration over the solid domain. Besides, a so-called sub-cell scheme is developed to smooth the discontinuity at the fluid-solid interface. The validity and accuracy of the proposed simulation method were examined well by applying it to the sedimentation problems of circular, triangular, square, as well as elliptic cylinders in a channel. An accuracy of 2nd order was observed, probably due to the use of triangular Lagrangian elements and consequently a piecewise-linear approximation of the rigid body shape and also due to the 2nd-order interpolation involved in the sub-cell scheme.