Navier-Stokes/Darcy模型的BDF2模块化梯度散度稳定格式的数值分析

Numerical Analysis of BDF2 Modular Grad-div Stabilization Method for the Navier-Stokes/Darcy Equations

Navier-Stokes/Darcy方程可用来模拟河流中的污染物对地下水的污染问题,以及血液在血管及器官间的渗透问题等,由于其在实际中的广泛应用,对其数值方法的研究受到广泛关注。提出了求解Navier-Stokes/Darcy方程的BDF2模块化梯度散度稳定数值格式,这种格式通过增加稳定化项,提高了解的有效性和精确性,在保留梯度散度稳定格式优点的同时,可以有效的避免大的稳定化参数对解的非正常影响,给出了格式的稳定性和误差分析。最后,通过数值算例验证了理论分析的正确性。

Navier Stokes/Darcy equation can be used to simulate the pollution of pollutants in rivers to groundwater,and the penetration of blood in blood vessels and organs.Due to its wide applications in practice,the research on the numerical method for Navier Stokes/Darcy equations has attracted extensive attention.A BDF2 modular gradient divergence stablized numerical scheme for solving Navier Stokes/Darcy equations is proposed.This scheme improves the validity and accuracy of the solution by adding a stabilization term.While retaining the advantages of the gradient divergence stable scheme,it can effectively avoid bad effects caused by large stabilization parameters.The stability and error analysis of the scheme are given.Finally,the correctness of the theoretical analysis is verified by numerical examples.