【摘要】 给出了数值求解初始变量不可压Navier Stokes/Euler耦合方程的一种分步块LU分解方法。与传统的时间分裂法不同,该法无需压力中介边条件,从而避免了传统时间分裂法要求的复杂的压力中介边条件逼近。分步块LU分解方法可看做经典的Uzawa算法的改进,后者曾被成功应用于不可压Navier Stokes/Euler耦合方程的求解。但本文显示分步块LU分解法比经典的Uzawa方法更经济。分析显示该法具有良好的稳定性和高精度,数值结果支持这一理论分析。更多还原

【Abstract】 A fractional step method for solving the incompressible NavierStokes/Euler coupled equations in primitive variables is analyzed as a block LU decomposition. In this formulation, no intermediate boundary conditions for the velocity and the pressure is required, in contrast to the traditional time splitting method. In addition, the fractional step method can be reviewed as an improvement of the classical Uzawa algorithm that has been proven to be useful in the calculation of the incompressible NavierStokes/Euler coupled equations. The fractional step method is showed to be cheaper than the classical Uzawa algorithm. The stability and the accuracy analysis are also given. Numerical results confirm the theoretical analysis. Simulations of the flow past the cylinder are carried out in order to demonstrate the potential applications of the NavierStokes/Euler coupled solver.更多还原