An Unstructured Finite-Volume Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids

Abstract

An unstructured finite-volume time-domain method (UFVTDM) is developed to solve two-dimensional transient heat conduction in multilayer functionally graded materials (FGMs). A four-node quadrilateral grid and a three-node triangular grid are employed to deal with mixed-grid problems. The accuracy of the method is improved by treating the quadrilateral grid as a bilinear element with consideration of both the linear term and the constant term. The improvement is validated to be vital to avoid violent numerical oscillation when applying the method to heat point-source problems. The accuracy and capability of the UFVTDM are validated by numerical tests.

Photothermal deflection of laser beam as means to characterize thermal properties of biological tissue: numerical study

“…Meanwhile, the ray trace method shows the magnitude of the photothermal deflection of laser beam through the acrylic block that depends on the thermal properties of the tissue sample. Standard techniques of numerical methodology for solving the governing equations for fluid flow and heat transfer are the finite-difference, finite-element, and finite-volume methods [10][11][12]. The finite-element and finite-volume methods are used to discretize the spatial domain into smaller volumes on the non-regular shape objects.…”

Finite-Volume Methods for Anisotropic Diffusion Problems on Skewed Meshes

“…For this test case, a steady and isotropic heat conduction problem [19] in a 2D plate is considered. The size of the computation domain is 5 m  10 m, and the heat diffusion coefficient K(x) ¼ 1 W=m C. The boundary conditions are defined by uðx; 0Þ ¼ uð0; yÞ ¼ 0 …”

High-Order Numerical Methods for 2D Parabolic Problems in Single and Composite Domains

“…Definition 1 (Discrete Auxiliary Problem (AP)). At time t i+1 , given the righthand side grid function q i+1 s : M 0 s → R, the following difference equations (34,35) are defined as the discrete AP.…”

“…Let us denote by G s ∆t,h F i+1 s the particular solution on N + s of the fully-discrete problem (33), defined by solving the AP (34,35) with…”

“…There is extensive existing work addressing numerical approximation of PDE posed on composite domains with interfaces or irregular domains, for example, the boundary integral method [11,56], difference potentials method [3,6,26,27,58,67], immersed boundary method [30,42,61,74], immersed interface method [2,46,47,49,69], ghost fluid method [31,32,50,51], the matched interface and boundary method [82,84,85,86], Cartesian grid embedded boundary method [19,41,57,83], multigrid method for elliptic problems with discontinuous coefficients on an arbitrary interface [18], virtual node method [9,39], Voronoi interface method [35,36], the finite difference method [8,10,24,75,78,79] and finite volume method [22,34] based on mapped grids, or cut finite element method [13,14,15,…”