A NEW EFFICIENT CONSERVATION-BASED METHOD FOR IMPLEMENTING POD-GALERKIN PROJECTION

The proper orthogonal decomposition (POD)-Galerkin method is an efficient method for quickly predicting the flow field and temperature field based on some given snapshots of physical fields at given conditions. It has been widely used in the field of flow and heat transfer engineering. In the POD-Galerkin method, the basis functions containing the main information of the physical field are extracted from a series of snapshots. And then the physical field with parameters under the design conditions can be quickly solved by a linear combination of the basis functions and corresponding spectral coefficients. The spectral coefficients of the basis functions can be obtained by solving the Galerkin projection equation. In this paper, a new conservative method to deal with the POD-Galerkin projection equation for heat conduction problems is proposed, which can ensure that the solved physical field can satisfy the conservative condition better with less numerical error and a quite coarse mesh. The major innovation point of the proposed method is the way for obtaining the spectral coefficients. In the proposed method they are obtained based on the conservation condition of each control volume. The numerical result obtained by this method has a very small error (within 10^-5 ℃ in the examples) compared with the finite volume method (FVM) solution even if there are only a few nodes in the basis functions. Some heat conduction examples are calculated to verify the effectiveness of the proposed method.