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A POD-based reduced-order finite difference extrapolating model for the non-stationary incompressible Boussinesq equations. (English) Zbl 1343.76031

Summary: A proper orthogonal decomposition (POD) method is used to establish a POD-based reduced-order finite difference (FD) extrapolating model with fully second-order accuracy for the non-stationary incompressible Boussinesq equations (NSIBEs). The error estimates of the POD-based reduced-order FD solutions obtained from the POD-based reduced-order FD extrapolating model are provided. The algorithm implementation for the POD-based reduced-order FD extrapolating model is given. A numerical experiment shows that the numerical results are consistent with the theoretical conclusions. Moreover, it is shown that the POD-based reduced-order FD extrapolating model is feasible and efficient for finding the numerical solutions for NSIBEs.

MSC:

76M20 Finite difference methods applied to problems in fluid mechanics
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
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