Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method (Advances in Applied Mathematics and Mechanics, 2018)
In this work, the hybrid solution reconstruction formulation proposed byLuo et al. [H. Luo, H. Dai, P. F. de Sousa and B. Yin, On the numerical oscillation of thedirect-forcing immersed-boundary method for moving boundaries, Computers & Fluids,56 (2012), pp. 61\u201376] for the finite-difference discretization on Cartesian meshesis implemented in the finite-element framework of the local domain-free discretization(DFD) method to reduce the numerical oscillations in the simulation of moving-boundaryflows. The reconstruction formulation is applied at fluid nodes in the immediatevicinity of the immersed boundary, which combines weightly the local DFDsolution with the specific values obtained via an approximation of quadratic polynomialin the normal direction to the wall. The quadratic approximation is associatedwith the no-slip boundary condition and the local simplified momentum equation.The weighted factor suitable for unstructured triangular and tetrahedral meshes isconstructed, which is related to the local mesh intervals near the immersed boundaryand the distances from exterior dependent nodes to the boundary. Therefore, the reconstructedsolution can account for the smooth movement of the immersed boundary.Several numerical experiments have been conducted for two- and three-dimensionalmoving-boundary flows. It is shown that the hybrid reconstruction approach can workwell in the finite-element context and effectively reduce the numerical oscillations withlittle additional computational cost, and the spatial accuracy of the original local DFDmethod can also be preserved.