论文标题
使用一般压力方程的不稳定粘性不可压缩流的数值模拟
Numerical simulations of unsteady viscous incompressible flows using general pressure equation
论文作者
论文摘要
在流体动力学中，一个重要的问题与流体压力的知识有关。最近，提出了另一种研究不可压缩液体流动的方法。它包括使用从可压缩的Navier-Stokes方程得出的一般压力方程（GPE）。在本文中，考虑了GPE并将其与Chorin的人造可压缩方法（ACM）和熵阻尼的人工压缩性（EDAC）方法进行了比较。这三种方法在交错的网格系统中被离散化，并在时间上以二阶为中心方案和及时的第三阶runge-kutta方案进行离散化。实现了三个测试用例：二维泰勒绿色涡流流，行动波和双重周期性剪切层。证明GPE是准确且有效的，可以捕获不稳定的不可压缩流的正确行为。 GPE获得的数值结果与ACM，EDAC和带有泊松方程的经典有限体积方法的数值非常吻合。此外，GPE收敛优于ACM收敛。提出的一般压力方程（GPE）允许解决一般，时间准确的，不可压缩的Navier-Stokes流。最后，从马赫和prandtl数字方面实现的参数研究表明，速度差异可以受任意最大值的限制，并且声波可以受阻。
In fluid dynamics, an important problem is linked to the knowledge of the fluid pressure. Recently, another approach to study incompressible fluid flow was suggested. It consists in using a general pressure equation (GPE) derived from compressible Navier-Stokes equation. In this paper, GPE is considered and compared with the Chorin's artificial compressibility method (ACM) and the Entropically damped artificial compressibility (EDAC) method. The three methods are discretized in a staggered grid system with second order centered schemes in space and a third order Runge-Kutta scheme in time. Three test cases are realized: two-dimensional Taylor-Green vortex flow, the traveling wave and the doubly periodic shear layers. It is demonstrated that GPE is accurate and efficient to capture the correct behavior for unsteady incompressible flows. The numerical results obtained by GPE are in excellent agreement with those obtained by ACM, EDAC and a classical finite volume method with a Poisson equation. Furthermore, GPE convergence is better than ACM convergence. The proposed general pressure equation (GPE) allows to solve general, time-accurate , incompressible Navier-Stokes flows. Finally, the parametric study realized in terms of Mach and Prandtl numbers shows that the velocity divergence can be limited by an arbitrary maximum and that acoustic waves can be damped.
