POD reduced-order model for steady natural convection based on a body-fitted coordinate

In this article, a POD reduced-order model for steady-state natural convection based on a body-fitted coordinate system is established. The velocity basis functions and temperature basis functions are generated, respectively. Based on the basis functions, the governing equations for velocity spectrum coefficient and temperature spectrum coefficient are deduced, which are coupled pluralistic quadratic nonlinear equations and solved iteratively by the Newton-Raphson method. Compared with the existing natural convection POD reduced-order models, the major advantage of the proposed POD model is its capability to calculate natural convections in different-shape domains having identical geometry characters. Two typical examples are given to show the model implementation procedure as well as to illustrate its good performance in terms of accuracy and robustness. It is found that even though the geometries and the physical conditions of the test cases differ greatly from those of the sampling cases, the reduced-order model can acquire accurate results efficiently.