Improvement of mass conservation and reduction of spurious oscillations for the local DFD method

Abstract

By introducing a mass source/sink term into the continuity equation, the mass-conservation property of the local domain-free discretisation (DFD) method is improved to reduce the spurious oscillations in the simulation of moving-boundary problems. The mass source/sink term is constructed by evaluating the mass flux through the solid part of the control volume split by the immersed boundary. Additionally, some special treatments are given for the multi-valued nodes associated with thin bodies. The introduction of source/sink term has also been extended to three-dimensional problems. Unlike the ghost-cell immersed boundary method, coupling the mass source/sink algorithm with the local DFD method is implemented on triangular and tetrahedral meshes. Compared to the hybrid reconstruction formulation, the properties of the original local DFD method can be preserved better. Numerical experiments for two-and three-dimensional moving-boundary problems show that the present mass source/sink treatment can reduce spurious oscillations effectively.

Extension of the local domain‐free discretization method to large eddy simulation of turbulent flows

“…When mass flux through the control surface associated with the node in the immediate vicinity of the IB (eg, K in Figure in two dimensions) is computed in the same way as a regular interior node, the mass conservation is satisfied in the control volume (enclosed by ABCD ) including a solid part, not exactly satisfied in the real fluid part. Zhang et al developed a mass source/sink technique to improve the mass‐conservation property of the DFD method for laminar flow computation. This technique is also employed in the present LES‐DFD method.…”

“…The extension of the aforementioned mass source/sink technique to three dimensions is straightforward. For more details, one can refer to the work of Zhang et al…”