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Reduction of Numerical Oscillations in Simulating Moving-Boundary Problems by the Local DFD Method

Published online by Cambridge University Press:  21 December 2015

Yang Zhang  and
Chunhua Zhou
Yang Zhang
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Chunhua Zhou*
Affiliation:
Department of Aerodynamics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
*
*Corresponding author. Email:chzhou@nuaa.edu.cn (C. H. Zhou)
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Abstract

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 moving-boundary 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.

Keywords

76D0576M99Numerical oscillationimmersed boundary methodmoving boundarydomain-free discretizationboundary condition
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 8 , Issue 1 , February 2016 , pp. 145 - 165
Copyright
Copyright © Global-Science Press 2016 

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