Numerical Computation of High Reynolds Number Cavity Flow Using SPH Method with Stream Function and Vorticity Formulation

TL;DR

This paper introduces a novel application of the SPH particle method to high Reynolds number cavity flow by reformulating Navier-Stokes equations with stream function and vorticity, successfully capturing fine flow structures.

Contribution

It is the first to apply the SPH method with stream function and vorticity formulation to high Reynolds number cavity flow, demonstrating its effectiveness.

Findings

Reproduction of small vortices in high Reynolds number flow

Validation of SPH method with stream function and vorticity formulation

Effective capture of fine flow structures

Abstract

When numerically computing high Reynolds number cavity flow, it is known that by formulating the Navier-Stokes equations using the stream function and vorticity as unknown functions, it is possible to reproduce finer flow structures. Although numerical computations applying methods such as the finite difference method are well known, to the best of our knowledge, there are no examples of applying particle-based methods like the SPH method to this problem. Therefore, we applied the SPH method to the Navier-Stokes equations, formulated with the stream function and vorticity as unknown functions, and conducted numerical computations of high Reynolds number cavity flow. The results confirmed the reproduction of small vortices and demonstrated the effectiveness of the scheme using the stream function and vorticity.