A dual interpolation precise integration boundary face method to solve two-dimensional transient heat conduction problems

Abstract

In this paper, we present a new numerical algorithm combining the dual interpolation boundary face method (DiBFM) with the precise integration method for solving the 2D transient heat conduction problem. In this new combined approach, the transient heat conduction problem is transformed from an initial boundary value problem to an initial value problem through a dual interpolation boundary face approach. This approach merges the conforming and nonconforming elements in the BFM implementation. Potentials and fluxes are approximated by the dual interpolation elements which include source and virtual points. Employing the moving-least-square approximation help to construct the constraint equations relating to virtual points. Then the analytical solution of the problem can be expressed by the matrix exponential function (MEF), which can be computed accurately through a precise integration method (PIM). The proposed numerical algorithm has been successfully implemented. Several numerical examples are given to illustrate the numerical accuracy and stability of the proposed method compared with the traditional precise integration boundary face method.