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.

构建ADI型有限体积方案以求解非经典的热传导方程。管中的原始3D模型在该域的很大一部分上都简化为混合尺寸模型。在3D和1D零件之间定义了特殊的界面条件。假定该解满足3D零件中的径向对称条件。有限体积方法用于近似空间微分算子，而ADI分裂用于时间积分。事实证明ADI方案是无条件稳定的。提出了一种有效的因式分解算法来求解所获得的方程组。计算实验的结果证实了理论误差分析。