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# Analysis of Unsteady Heat Transfer Problems with Complex Geometries Using Isogeometric Boundary Element Method

Weihua Fang1, Zhilin An2, Tiantang Yu2, *, Tinh Quoc Bui3, 4, *

1 Nanjing Automation Institute of Water Conservancy and Hydrology, Nanjing, 210012, China.
2 Department of Engineering Mechanics, Hohai University, Nanjing, 211100, China.
3 Institute for Research and Development, Duy Tan University, Da Nang City, Vietnam.
4 Department of Civil and Environmental Engineering, Tokyo Institute of Technology, 2-12-1-W8-22, Ookayama, Meguro-ku, Tokyo 152-8552, Japan.

* Corresponding Authors: Tiantang Yu. Email: ;
Tinh Quoc Bui. Email: .

Computers, Materials & Continua 2020, 62(2), 929-962. https://doi.org/10.32604/cmc.2020.05022

## Abstract

Numerical analysis of unsteady heat transfer problems with complex geometries by the isogeometric boundary element method (IGABEM) is presented. The IGABEM possesses many desirable merits and features, for instance, (a) exactly represented arbitrarily complex geometries, and higher-order continuity due to nonuniform rational B-splines (NURBS) shape functions; (b) using NURBS for both field approximation and geometric description; (c) directly utilizing geometry data from computer-aided design (CAD); and (d) only boundary discretization. The formulation of IGABEM for unsteady heat transfer is derived. The domain discretization in terms of IGABEM for unsteady heat transfer is required as that in traditional BEM. The internal values however are obtained with the analytical formula according to the values on the boundaries, and its computations are therefore mainly dependent on the discretization of the boundaries. The coordinates of internal control points are obtained with the coordinates of control points on the boundaries using Coons body interpolation method. The developed approach is tested with several numerical examples from simple to complicated geometries. Good agreement is gained with reference solutions derived from either analytical or finite element methods.

## Keywords

W. Fang, Z. An, T. Yu and T. Quoc Bui, "Analysis of unsteady heat transfer problems with complex geometries using isogeometric boundary element method," Computers, Materials & Continua, vol. 62, no.2, pp. 929–962, 2020.

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