非定常Stokes方程的降阶稳定化CN有限体积元外推模型

A Reduced-Order Stabilized CNFVE Extrapolating Model for Non-Stationary Stokes Equations

利用稳定化的Crank-Nicolson(CN)有限体积元方法和特征投影分解方法,建立非定常Stokes方程的一种自由度很少、精度足够高的降阶稳定化CN有限体积元外推模型,并给出这种降阶稳定化CN有限体积元外推模型解的误差估计和算法的实现.最后用数值例子说明数值结果与理论结果相吻合,并阐明这种降阶稳定化CN有限体积元外推模型的优越性.

A reduced-order stabilized Crank-Nicolson finite volume element （SCNFVE） extrapolating model with sufficiently high accuracy and few degrees of freedom for non-stationary Stokes equations was established by means of the SCNFVE method and the proper orthogonal decompostion （POD） technique. The error estimates of the reduced-order approximate solutions and the algorithm implementation for the reduced-order SCNFVE extrapolating model were provided. Finally, a numerical example of conduit flow indicates that the results of the proposed model are consistent with those of the theoretical solution. Moreover, the advantages of lower computation complexity and higher calculation accuracy of the reduced-order SCNFVE extrapolating model are shown in comparison with the classical methods.