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Title: Navier–Stokes Characteristic Boundary Conditions Using Ghost Cells

Abstract

Solution methods for the compressible Navier–Stokes equations based on finite volume discretizations often implement boundary conditions using ghost cells outside of the computational domain. Filling the ghost cells using straightforward zeroth-or first-order extrapolation, although computationally expedient, is well known to fail even for some simple flows, especially when turbulent structures interact with the boundaries or if time-varying inflow conditions are imposed. The Navier–Stokes characteristic boundary condition approach provides more accurate boundary conditions, but requires the use of special discretizations at boundaries. The present paper develops a new technique based on the Navier–Stokes characteristic boundary condition approach to derive values for ghost cells that significantly improve the treatment of boundaries over simple extrapolation, but retain the ghost cell approach. Furthermore, it is demonstrated in the context of a Godunov integration procedure that the new method provides accurate results, while allowing the use of the same stencil and numerical methodology near the boundaries as in the interior.

Authors:
 [1];  [1];  [1]
  1. Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Publication Date:
Research Org.:
Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1525185
Grant/Contract Number:  
AC02-05CH11231
Resource Type:
Accepted Manuscript
Journal Name:
AIAA Journal
Additional Journal Information:
Journal Volume: 55; Journal Issue: 10; Journal ID: ISSN 0001-1452
Publisher:
AIAA
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING

Citation Formats

Motheau, Emmanuel, Almgren, Ann, and Bell, John B. Navier–Stokes Characteristic Boundary Conditions Using Ghost Cells. United States: N. p., 2017. Web. doi:10.2514/1.J055885.
Motheau, Emmanuel, Almgren, Ann, & Bell, John B. Navier–Stokes Characteristic Boundary Conditions Using Ghost Cells. United States. doi:10.2514/1.J055885.
Motheau, Emmanuel, Almgren, Ann, and Bell, John B. Tue . "Navier–Stokes Characteristic Boundary Conditions Using Ghost Cells". United States. doi:10.2514/1.J055885. https://www.osti.gov/servlets/purl/1525185.
@article{osti_1525185,
title = {Navier–Stokes Characteristic Boundary Conditions Using Ghost Cells},
author = {Motheau, Emmanuel and Almgren, Ann and Bell, John B.},
abstractNote = {Solution methods for the compressible Navier–Stokes equations based on finite volume discretizations often implement boundary conditions using ghost cells outside of the computational domain. Filling the ghost cells using straightforward zeroth-or first-order extrapolation, although computationally expedient, is well known to fail even for some simple flows, especially when turbulent structures interact with the boundaries or if time-varying inflow conditions are imposed. The Navier–Stokes characteristic boundary condition approach provides more accurate boundary conditions, but requires the use of special discretizations at boundaries. The present paper develops a new technique based on the Navier–Stokes characteristic boundary condition approach to derive values for ghost cells that significantly improve the treatment of boundaries over simple extrapolation, but retain the ghost cell approach. Furthermore, it is demonstrated in the context of a Godunov integration procedure that the new method provides accurate results, while allowing the use of the same stencil and numerical methodology near the boundaries as in the interior.},
doi = {10.2514/1.J055885},
journal = {AIAA Journal},
number = 10,
volume = 55,
place = {United States},
year = {2017},
month = {7}
}

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