An explicit meshless point collocation solver for incompressible Navier-Stokes equations

TL;DR

This paper introduces a meshless point collocation explicit solver for 2D incompressible Navier-Stokes equations, demonstrating high accuracy and efficiency in complex geometries without mesh generation.

Contribution

It presents a novel meshless point collocation method for explicit solution of Navier-Stokes equations, suitable for complex geometries and comparable in stability to implicit methods.

Findings

Accurate results for benchmark flows like lid-driven cavity and vortex shedding.

Effective handling of complex geometries such as obstacles and bifurcations.

High computational efficiency with stable time steps.

Abstract

We present a strong form, meshless point collocation explicit solver for the numerical solution of the transient, incompressible, viscous Navier-Stokes (N-S) equations in two dimensions. We numerically solve the governing flow equations in their stream function-vorticity formulation. We use a uniform Cartesian embedded grid to represent the flow domain. We compute the spatial derivatives using the Meshless Point Collocation (MPC) method. We verify the accuracy of the numerical scheme for commonly-used benchmark problems including lid-driven cavity flow, flow over a backward-facing step and vortex shedding behind a cylinder. We have examined the applicability of the proposed scheme by considering flow cases with complex geometries, such as flow in a duct with cylindrical obstacles, flow in a bifurcated geometry, and flow past complex-shaped obstacles. Our method offers high accuracy and excellent computational efficiency as demonstrated by the verification examples, while maintaining a stable time step comparable to that used in unconditionally stable implicit methods.