A dual interpolation boundary face method for three-dimensional potential problems. (September 2019)

• Record Type: Journal Article
• Authors: Zhang, Jianming; Chi, Baotao; Lin, Weicheng; Ju, Chuanming
• Is Part Of: International journal of heat and mass transfer. Volume 140(2019)
• Page Start: 862
• Page End: 876
• Publication Date: 2019-09
• Subjects: Potential problems -- Dual interpolation -- Boundary face method -- Boundary element method -- Moving least-squares approximation; Heat -- Transmission -- Periodicals; Mass transfer -- Periodicals; Chaleur -- Transmission -- Périodiques; Transfert de masse -- Périodiques; Electronic journals; 621.4022
• DOI: 10.1016/j.ijheatmasstransfer.2019.06.011
• Languages: English
• ISSNs: 0017-9310

Abstract

Highlights: The DiBFM has been presented for solving three-dimensional potential problems. A new type of elements named the dual interpolation elements are proposed in DiBFM. The DiBFM can unify the conventional continuous and discontinuous elements. Even with some irregular elements, the DiBFM can exhibit high accuracy behavior. The DiBFM is flexible to handle real world geometries in a fully automated manner. Abstract: A dual interpolation boundary face method (DiBFM) is presented for solving three-dimensional potential problems. The DiBFM is an alternative implementation of the boundary face method (BFM) and inherits all the merits of BFM, which has been proposed to unify the continuous and discontinuous elements, improve the accuracy of the interpolation calculation and alleviate the heavy task of mesh generation. The DiBFM implementation is based on a new type of elements, called the dual interpolation elements, in which the nodes are classified into virtual nodes and source nodes. Despite the introduction of virtual nodes in the dual interpolation elements, only source nodes of each element are taken as the collocation points. Corresponding constraint equations using the MLS approximation are formulated to condense the degrees of freedom for all virtual nodes, which does not result in the scale of final linear system increasing. In addition, even with some irregular elements in numerical simulation, accurate results and high convergence rates can be achieved by the DiBFM. The DiBFM is flexible and convenient to handle more complicated, real world structures without any geometric simplification in a fully automated manner. Numerical results have demonstrated the validity, high accuracy and superior convergence of the proposed method.