Finite Volume Implementation of the Method of Asymptotic Partial Domain Decomposition for the Heat Equation on a Thin Structure

The unsteady heat equation is considered in thin structures. The asymptotic expansion of the solution constructed earlier is used to evaluate partial derivatives of the solution. The method of partial asymptotic domain decomposition is applied to the unsteady heat equation. It reduces the original 2D model to a hybrid dimension one, partially 2D, partially 1D with some special interface conditions between the 2D and 1D parts. The finite volume method is applied to numerically solve the hybrid dimension model. The error estimate is established. A numerical experiment confirms the theoretical error evaluation.