粘弹性流体模拟的DCQ-QUICK格式

Simulating Viscoelastic Flow Field Based on DCQ-QUICK Scheme

流场中对流项的离散是其数值求解的一大难点.本文基于非结构同位网格格心有限体积法,针对流场守恒方程与Oldroyd-B本构方程的对流项,提出了一种耦合高阶Q-QUICK格式的延迟修正格式.通过平面Poiseuille流在不同We数下数值解与解析解的比较,验证了该方法具有较高的精度和较好的数值稳定性.通过4:1粘弹性收缩流的数值模拟,揭示了不同Re、We数下流场中压力、应力变化及角涡生长情况,同时也表明了该方法可有效扩大We数的计算范围.

The discrete for the convection term is one of the main di？culties for the num-erical solution of viscoelastic fluid flow. In this paper, for the conservation equations and the Oldroyd-B constitutive equation, a deferred correction method coupled with high order Q-QUICK scheme for the computation of the convection flux is proposed. This method is designed based on the finite volume method on unstructured collocated grids. The planar poiseuille viscoelastic flow is simulated numerically to verify the high precision and stability of the proposed method. In the simulation of 4：1 contraction viscoelastic flow, the changes of the stream lines and stresses as well as growing of the salient corner vortex versus the Weissenberg numbers are revealed. The numerical results show that the numerical method is capable of expanding the range of the Weissenberg numbers for nonlinear viscoelastic fluid.