一种基于压力泊松方程的流体结构紧耦合算法

从流固耦合系统的整体控制方程出发,推导出与流体控制方程一致的耦合等价方程,并得到基于耦合方程的压力泊松方程,通过求解耦合系统压力泊松方程和一致的等价方程就能获得耦合系统的解,而不需要直接求解整体耦合系统的控制方程,有利于降低求解自由度。预估-校正多步迭代格式用于耦合系统的时间推进,克服了传统迭代耦合方法由于时间不同步而产生较大数值误差的不足。应用该方法对附带局部突起的主动脉弓动脉瘤进行流固耦合分析,验证数值方法的可行性。

A MONOLITHIC FLUID-STRUCTURE INTERACTION APPROACH BASED ON THE PRESSURE POISSON EQUATION

A monolithic coupling approach to solve the fluid-structure interaction(FSI) problem is presented.The consistent coupling equation is derived from the whole control equation for FSI;also,the pressure Poisson equation(PPE) for FSI is derived.The solution of whole coupling system is gained by solving the PPE and the consistent coupling equation.The approach presented can decrease the degree of freedom(DOF) of solving equations because it does not require solving the whole control equation.The time integration is based on the algorithm of predictor-multi-corrector,which can decrease the numerical error compared with the traditional loosed coupling method.To demonstrate the performance of the proposed approach,an idealized aneurysm model was constructed and the proposed method was employed to perform the FSI simulation of physiological blood flow in the aneurysm model.The results show the validity of the proposed numerical approach.