Analysis of the Pressure-Velocity boundary conditions for the projection method solution of the incompressible Navier-Stokes Equations

TL;DR

This paper investigates the effects of pressure-tangential-velocity boundary conditions on the projection method for solving incompressible Navier-Stokes equations, aiming to improve boundary treatment accuracy.

Contribution

It introduces and analyzes a pressure-tangential-velocity boundary condition approach within the projection method framework for incompressible flow simulations.

Findings

Enhanced understanding of boundary condition impacts on solution accuracy

Identification of conditions for stable and accurate boundary implementation

Guidelines for applying pressure-tangential-velocity boundary conditions

Abstract

The projection method is the standard approach for numerically integrating the incompressible Navier-Stokes equation initial-boundary-value problem. Typical boundary conditions specify either the velocity or the gradient velocity on the boundary. Here, we consider the pressure-tangential-velocity boundary condition in which the tangential components of the velocity and the pressure at the boundary are specified.