To read this content please select one of the options below:

A novel and efficient approach to specifying Dirichlet far-field boundary condition of pressure Poisson equation

Jun-Hyeok Lee (Department of Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Korea)
Seung-Jae Lee (Research Institute of Marine Systems Engineering, Seoul National University, Seoul, Korea)
Jung-chun Suh (Naval Architecture and Ocean Engineering, Seoul National University, Seoul, Korea)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Article publication date: 5 March 2018

125

Abstract

Purpose

As the penalized vortex-in-cell (pVIC) method is based on the vorticity-velocity form of the Navier–Stokes equation, the pressure variable is not incorporated in its solution procedure. This is one of the advantages of vorticity-based methods such as pVIC. However, dynamic pressure is an essential flow property in engineering problems. In pVIC, the pressure field can be explicitly evaluated by a pressure Poisson equation (PPE) from the velocity and vorticity solutions. How to specify far-field boundary conditions is then an important numerical issue. Therefore, this paper aims to robustly and accurately determine the boundary conditions for solving the PPE.

Design/methodology/approach

This paper introduces a novel non-iterative method for specifying Dirichlet far-field boundary conditions to solve the PPE in a bounded domain. The pressure field is computed using the velocity and vorticity fields obtained from pVIC, and the solid boundary conditions for pressure are also imposed by a penalization term within the framework of pVIC. The basic idea of our approach is that the pressure at any position can be evaluated from its gradient field in a closed contour because the contour integration for conservative vector fields is path-independent. The proposed approach is validated and assessed by a comparative study.

Findings

This non-iterative method is successfully implemented to the pressure calculation of the benchmark problems in both 2D and 3D. The method is much faster than all the other methods tested without compromising accuracy and enables one to obtain reasonable pressure field even for small computation domains that are used regardless of a source distribution (the right-hand side in the Poisson equation).

Originality/value

The strategy introduced in this paper provides an effective means of specifying Dirichlet boundary conditions at the exterior domain boundaries for the pressure Poisson problems. It is very efficient and robust compared with the conventional methods. The proposed idea can also be adopted in other fields dealing with infinite-domain Poisson problems.

Keywords

Acknowledgements

This research was supported by the Industrial Convergence Strategic Technology Development Program (no. 10044499) funded by the Ministry of Trade, Industry & Energy (MOTIE, Korea) and the National Research Foundation of Korea (NRF-2015R1D1A1A020617130).

Citation

Lee, J.-H., Lee, S.-J. and Suh, J.-c. (2018), "A novel and efficient approach to specifying Dirichlet far-field boundary condition of pressure Poisson equation", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 28 No. 3, pp. 726-744. https://doi.org/10.1108/HFF-02-2017-0060

Publisher

:

Emerald Publishing Limited

Copyright © 2018, Emerald Publishing Limited

Related articles