A REDUCED FINITE DIFFERENCE SCHEME BASED ON PROPER ORTHOGONAL DECOMPOSITION FOR THE NONSTATIONARY CONDUCTION--CONVECTION PROBLEMS
热传导对流方程基于POD的差分格式

In this work, the nonstationary conduction--convection equations are studied with singular value decomposition and proper orthogonal decomposition (POD). A reduced finite difference scheme (FDS) based on POD for the nonstationary conduction--convection equations is presented. And the error estimates between usual finite difference solutions and POD solutions of reduced FDS are analyzed. It is shown by considering the results obtained for numerical simulations of cavity flows that the errors between POD solutions of reduced FDS and usual finite difference solutions are consistent with theoretical results. Moreover, it is also shown that POD method is feasible and efficient in numerical solutions for the nonstationary conduction--convection equations.