用密度函数法对自由表面进行数值模拟

Density-function method for simulation of flow with unsteady free surface

本文从二维非定常N S方程出发,提出了一种处理自由表面问题的数值方法。引入密度函数法(density func tionmethod)追踪自由表面,在密度函数的传输方程中采用TVD格式达到了二阶精度。对均匀来流中的非定常不可压方柱绕流进行了数值模拟。数值结果成功地捕捉了自由表面波动以及漩涡的生成、分离的时间发展历程,同时验证了本方法的有效性。

A numerical method for free surface problem by using the two-dimensional unsteady incompressible Navier-Stokes equations was proposed in present paper. To capture the free surface the density-function method was employed. TVD scheme was used to solve the transport equation of the density function to obtain second order spatial accuracy. The unsteady incompressible viscous flows around a square cylinder in uniform stream was computed. The numerical solutions successfully captured the free surface, vortex generation, separation and evolution induced by the submerged cylinder. The validity of the method to treat strongly nonlinear phenomena is verified.