正则化δ函数对浸入边界法精度的影响

浸入边界法是对流固耦合系统进行数学建模和数值模拟的有效工具，在生物力学领域的应用尤为广泛．正则化δ函数对精度的影响是研究浸入边界法本身性质的一个重要课题．采用虚拟解法对此展开分析．首先使用光滑虚拟解证明程序的正确性，然后使用压力存在跳跃的虚拟解研究浸入边界法的精度．通过分析使用4种不同的正则化δ函数时整个流场的离散误差，得到以下结论:浸入边界法只具有1阶精度；选用不同的正则化δ函数，不能提高浸入边界法的精度，但会影响整个流场的离散误差值．

Effect of the Regularized Delta Function on the Accuracy of the Immersed Boundary Method

The immersed boundary method was an effective technique for modeling and simulating fluid-structure interactions especially in the area of biomechanics. The effect of the regularized delta function on its accuracy was an important subject in the property study. The method of manufactured solutions was taken as the research means. The computational code was firstly verified to be mistaken free by using smooth manufactured solutions. Then a jump in the manufactured solution for pressure was introduced to study the accuracy of the immersed boundary method. Four kinds of the regularized delta function were taken to test its effects on accuracy analysis. By analyzing the discretization errors, the accuracy of the immersed boundary method was proved to be first order. Meanwhile, the results showed that the regularized delta function could not improve the accuracy, but could change the discretization errors on the entire computational domain.