GREENS-FUNCTION BASED INTEGRAL APPROACHES TO LINEAR TRANSIENT BOUNDARY-VALUE-PROBLEMS AND THEIR STABILITY CHARACTERISTICS (I)

Two Green's function-based formulations are applied to the governing d ifferential equation which describes unsteady heat or mass transport i n an isotropic homogeneous 1-D domain. In this first part of a two ser ies of papers, the linear form of the differential equation is address ed. The first formulation, herein denoted the quasi-steady Green eleme nt (QSGE) formulation, uses the Laplace differential operator as auxil iary equation to obtain the singular integral representation of the go verning equation, while the second, denoted the transient Green elemen t (TGE), uses the transient heat equation as auxiliary equation. The m athematical simplicity of the Green's function of the first formulatio n enhances the ease of solution of the integral equations and the resu ltant discrete equations. From the point of computational convenience, therefore, the first formulation is preferred. The stability characte ristics of the two formulations are evaluated by examining how they pr opagate various Fourier harmonics in speed and amplitude. We found tha t both formulations correctly reproduce the theoretical speed of the h armonics, but fail to propagate the amplitude of the small harmonics c orrectly for Courant value of about unity. The QSGE formulation with d ifference weighting values between 0.67 and 0.75, and the TGE formulat ion provide optimal performance in numerical stability. (C) 1998 Elsev ier Science Inc. All rights reserved.