粘性不可压缩流动的投影稳定化方法

Stabilized Projection Methods for Viscous Incompressible Flows

利用压力投影和梯度投影稳定化方法的思想,对高雷诺数下的粘性不可压缩流动的最低阶元给出了一种稳定的有限元格式.该格式不但绕开了inf-sup条件的限制,并且克服了当雷诺数很大时造成的不稳定性.利用不动点原理证明了解的存在唯一性,给出了误差估计.误差结果表明,该方法能达到最优精度.

Combining the best features of pressure projection and gradient projection,we present a new stabilization method for the incompressible Navier-Stokes equations with a high Reynolds number based on the lowest order velocity-pressure pairs.The scheme ameliorates the restrictive inf-sup condition and overcomes convection dominated.The existence and uniquence are proved.Furthermore,the error estimation results show that it achieve optimal accuracy with respect to solution regularity.