Parallel implementation of a VIScous Vorticity Equation (VISVE) method in 3-D laminar flow

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. (C) 2020 Elsevier Inc. All rights reserved.

Automated summary

This paper introduces a newly developed parallel implementation for solving the 3-D vorticity equation in order to fully simulate incompressible laminar flow. The method efficiently handles 3-D problems with irregular wall boundaries in small computational domains. By discretizing the curl form of vorticity equation using the Finite Volume Method and applying Stokes' theorem, the approach ensures divergence-free vorticity field and recovers vorticity-preserving velocity field through specific schemes.