ADI scheme for partially dimension reduced heat conduction models

Abstract

The ADI type finite volume scheme is constructed to solve the non-classical heat conduction equation. The original 3D model in a tube is reduced to a hybrid dimension model in a large part of the domain. Special interface conditions are defined between 3D and 1D parts. It is assumed that the solution satisfies radial symmetry conditions in 3D parts. The finite volume method is applied to approximate spatial differential operators and ADI splitting is used for time integration. It is proved that the ADI scheme is unconditionally stable. Efficient factorization algorithm is presented to solve the obtained systems of equations. Results of computational experiments confirm the theoretical error analysis.