In this work, the hybrid solution reconstruction formulation proposed by
Luo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of the
direct-forcing immersed-boundary method for moving boundaries, Computers & Fluids,
56 (2012), pp. 61–76] for the finite-difference discretization on Cartesian meshes
is implemented in the finite-element framework of the local domain-free discretization
(DFD) method to reduce the numerical oscillations in the simulation of movingboundary
flows. The reconstruction formulation is applied at fluid nodes in the immediate
vicinity of the immersed boundary, which combines weightly the local DFD
solution with the specific values obtained via an approximation of quadratic polynomial
in the normal direction to the wall. The quadratic approximation is associated
with the no-slip boundary condition and the local simplified momentum equation.
The weighted factor suitable for unstructured triangular and tetrahedral meshes is
constructed, which is related to the local mesh intervals near the immersed boundary
and the distances from exterior dependent nodes to the boundary. Therefore, the reconstructed
solution can account for the smooth movement of the immersed boundary.
Several numerical experiments have been conducted for two- and three-dimensional
moving-boundary flows. It is shown that the hybrid reconstruction approach can work
well in the finite-element context and effectively reduce the numerical oscillations with
little additional computational cost, and the spatial accuracy of the original local DFD
method can also be preserved.