Space-time backward substitution method for nonlinear transient heat conduction problems in functionally graded materials

Abstract

In this paper, an efficient space-time backward substitution method (STBSM) is presented for solving nonlinear transient heat conduction problems in 2D and 3D functionally graded materials (FGMs). To improve the computation efficiency of the traditional backward substitution method (BSM) for transient problems, the space-time radial basis function (STRBF) and space-time trigonometric basis function (STTBF) are introduced for interpolation in the proposed method. The time dimension is regarded as a pseudo-space dimension to generate the space-time Euler metric r T in STRBF, which can be applied to transform the d -dimensional transient governing equation into ( d + 1 ) -dimensional steady-state governing equation. Benefiting from merits of the traditional BSM, an accurate numerical solution is available with only a few of computational points. Several examples are solved to verify the accuracy and efficiency of the proposed method and its merits and flaws are discussed in the end. • A space-time method is attempted for 2D and 3D heat conduction problems in FGMs. • Space-time domain and space-time radial basis function are introduced into backward substitution method. • By introducing pseudo-space-time dimension to transform the origin transient problem into steady-state problem. • The proposed method has excellent computational efficiency.