This paper presents a newly developed parallel implementation of solving the 3–D vorticity equation to fully simulate the incompressible laminar flow in the Eulerian frame. This method is designed to solve 3–D problems with irregular wall boundaries in small and compact computational domains in general shapes efficiently. The curl form of vorticity equation is discretized using the Finite Volume Method (FVM) by applying Stokes' theorem, which automatically guarantees the divergence–free condition of vorticity field at all times. The vorticity preserving velocity field is recovered by an explicit scheme without solving any linear system, and this velocity field is reprojected onto a divergence–free space by solving only one scalar velocity–potential Poisson's equation. The vorticity boundary condition is satisfied by employing a vorticity creation scheme, that can handle arbitrary wall boundary shapes. Numerical results of the flow past a 3–D NACA0012 hydrofoil with one periodic direction, the flow past a sphere, and the flow past a 3–D rectangular wing are presented to validate the scheme.

本文介绍了一种新近开发的并行解决方案，它可以解决3D涡度方程，从而完全模拟欧拉框架中不可压缩的层流。此方法旨在有效解决一般形状较小而紧凑的计算域中具有不规则墙边界的3D问题。利用斯托克斯定理，使用有限体积法（FVM）将涡旋方程的卷曲形式离散化，该定理可自动保证旋涡场始终无散度。保留涡度的速度场是通过一种显式方案恢复的，无需求解任何线性系统，并且仅通过求解一个标量速度-势泊松方程即可将该速度场重新投影到无散度的空间。通过采用可以处理任意壁边界形状的涡度创建方案，可以满足涡度边界条件。提出了以一个周期性方向通过3D NACA0012水翼的流动，通过球体的流动以及通过3D矩形翼的流动的数值结果，以验证该方案。