边界数据浸入法在弱可压缩流动中的应用

Application of boundary data immersion method in weak compressible flow

受限于计算机的计算能力与计算的成本,实际的计算过程中,往往要对流体做出一些物理假设,如无粘流体、不可压缩流体等,但是这将给计算带来不同程度的误差.为解决此问题,提出了一种对弱可压缩粘性流动问题进行求解的数值方法.该方法不仅可以对计算域内包含静止固体的流场进行计算,也适用于包含运动固体的弱可压缩粘性流场的求解.该方法从水的状态方程开始,对弱可压缩粘性流体运动的速度与压力方程进行了严格推导.考虑到流场中固体的影响,使用边界数据浸入法(Boundary Data Immersion Method, BDIM)将流体子域与固体子域之间耦合,而所使用的BDIM可将流体及水下声学计算中的运动物体准确地表示出来.因此,本文首次将弱可压缩粘性流动计算与BDIM结合起来,并解决了考虑流体的弱可压缩性与粘性的流场求解问题.为验证所提方法的有效性及准确性,计算了3个二维经典算例,并将计算结果与采用其他方法所得数据结果进行比较.对比结果表明,在考虑流体的弱可压缩性与粘性的前提下,本文所提出的新算法可对运动流体中存在静止或运动固体的流场进行准确有效的计算.

Limited to the calculation capability of computers and computational cost,some physical assumptions for flows are needed in the realistic simulation,such as inviscid flow,incompressible flow and so on,which will take various degrees of error in the simulation results.To solve this problem,a numerical method used to solve the weak compressible viscous flow is presented here that is capable to solve the weak compressible viscous flow whether there is a static or moving solid body in the flow field.Starting from the state equation of water,the velocity and pressure governing equations for weak compressible viscous flows are derived rigorously.Considering the effect of solid body,the Boundary Data Immersion Method(BDIM),which can accurately represent moving bodies in flow and underwater acoustic simulations,is employed to couple the fluid sub-domain and solid sub-domain.Therefore,the flow field with the effects of the compression and viscosity is solved by coupling the weak compressible viscous flow and the BDIM.The effectiveness and accuracy of our method are validated by three two dimensional cases,and the results indicate that the novel method simulates the flow flied accurately and effectively for both a static and moving solid body.