Study on a BFC-Based POD-Galerkin Reduced-Order Model for the Unsteady-State Variable-Property Heat Transfer Problem

A proper orthogonal decomposition-reduced-order model (POD-ROM) method for unsteady-state heat conduction problems with variable physical properties is developed based on the body-fitted coordinate. Two mathematically equivalent forms of the ROM are derived, but their performance is quite different for finite volume. It is found that to obtain accurate prediction by the POD-ROM, the operators of the Jacobi factor and other variables in the ROM should be consistent with those in the finite-volume method (FVM). Validated by a complicated unsteady-state heat conduction problem, the established ROM can obtain accurate prediction of the unsteady-state heat conduction problem with variable properties in which the maximum ratio of thermal conductivity reaches 333.