ARS | Publication request: Boundary treatments for 2D elliptic mesh generation in complex geometries

Submitted to: Journal of Computational Physics 2
Publication Type: Peer Reviewed Journal
Publication Acceptance Date: May 1, 2008
Publication Date: July 1, 2008
Citation: Zhang, Y., Jia, Y., Wang, S.S., Chan, H. 2008. Boundary treatments for 2D elliptic mesh generation in complex geometries. Journal of Computational Physics 2. 227(16):7977-7997.

Interpretive Summary: In Computational Fluids Dynamics (CFD), complex geometries remain a challenge not only in numerical simulation but also in mesh generation. In this study, a boundary treatment method is proposed for two dimensional elliptic mesh generation in geometrically complex domains. The present method applies the Neumann-Dirichlet boundary conditions and consists of three components: (1) an auxiliary mesh constructed with the boundary line and the neighboring mesh line; (2) boundary curvature corrections using a second-order parabolic interpolation; and (3) weighting of the boundaries according to the boundary curvatures. First, the boundary nodes are driven by solving the auxiliary mesh, then they are corrected by the parabolic interpolation; and, finally they are adjusted by the weights of the boundary. Numerical simulations have indicated that the width of the auxiliary mesh which is controlled by a scale parameter that has more effects on mesh smoothness rather than mesh orthogonality. Also, the present method is not sensitive to the initial conditions. Examples and applications have demonstrated that the present method can significantly improve mesh quality both in mesh orthogonality and smoothness. The drawback of the present method is that more computation efforts are needed which will slow down the whole computation.

Technical Abstract: This paper presents a boundary treatment method for 2D elliptic mesh generation in complex geometries. Corresponding to Neumann- Dirichlet boundary conditions (sliding boundary conditions), the proposed method aims at achieving orthogonal and smooth nodal distribution along irregular boundaries. In this method, a three-lined wide auxiliary mesh composed of the boundary line, an auxiliary line generated by its neighboring mesh line and itself, and the reflection of this auxiliary line is constructed so that the movements of the boundary nodes are driven by solving this auxiliary mesh. The boundary nodes are further corrected and adjusted by a second-order parabolic interpolation method and the weights of the boundary, respectively. The proposed method was demonstrated through examples, and also applied to complex domains in fields. It has been shown that this method is able to produce high quality meshes in domains with complex geometries