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Title: High-order, stable, and conservative boundary schemes for central and compact finite differences

Abstract

Stable and conservative numerical boundary schemes are constructed such that they do not diminish the overall accuracy of the method for interior schemes of orders 4, 6, and 8 using both explicit (central) and compact finite differences. Previous attempts to develop stable numerical boundary schemes for non-linear problems have resulted in schemes which significantly reduced the global accuracy and/or required some form of artificial dissipation. Thus, the schemes developed in this paper are the first to not require this tradeoff, while also ensuring discrete conservation and allowing for direct boundary condition enforcement. After outlining a general procedure for the construction of conservative boundary schemes of any order, a simple, yet novel, optimization strategy which focuses directly on the compressible Euler equations is presented. Furthermore, the result of this non-linear optimization process is a set of high-order, stable, and conservative numerical boundary schemes which demonstrate excellent stability and convergence properties on an array of linear and non-linear hyperbolic problems.

Authors:
ORCiD logo [1]; ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1493552
Report Number(s):
LA-UR-17-21169
Journal ID: ISSN 0045-7930
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Computers and Fluids
Additional Journal Information:
Journal Volume: 183; Journal ID: ISSN 0045-7930
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; high-order; conservative; hyperbolic; stability; non-linear; boundaries; finite difference; optimization

Citation Formats

Brady, Peter T., and Livescu, Daniel. High-order, stable, and conservative boundary schemes for central and compact finite differences. United States: N. p., 2018. Web. doi:10.1016/j.compfluid.2018.12.010.
Brady, Peter T., & Livescu, Daniel. High-order, stable, and conservative boundary schemes for central and compact finite differences. United States. doi:10.1016/j.compfluid.2018.12.010.
Brady, Peter T., and Livescu, Daniel. Thu . "High-order, stable, and conservative boundary schemes for central and compact finite differences". United States. doi:10.1016/j.compfluid.2018.12.010.
@article{osti_1493552,
title = {High-order, stable, and conservative boundary schemes for central and compact finite differences},
author = {Brady, Peter T. and Livescu, Daniel},
abstractNote = {Stable and conservative numerical boundary schemes are constructed such that they do not diminish the overall accuracy of the method for interior schemes of orders 4, 6, and 8 using both explicit (central) and compact finite differences. Previous attempts to develop stable numerical boundary schemes for non-linear problems have resulted in schemes which significantly reduced the global accuracy and/or required some form of artificial dissipation. Thus, the schemes developed in this paper are the first to not require this tradeoff, while also ensuring discrete conservation and allowing for direct boundary condition enforcement. After outlining a general procedure for the construction of conservative boundary schemes of any order, a simple, yet novel, optimization strategy which focuses directly on the compressible Euler equations is presented. Furthermore, the result of this non-linear optimization process is a set of high-order, stable, and conservative numerical boundary schemes which demonstrate excellent stability and convergence properties on an array of linear and non-linear hyperbolic problems.},
doi = {10.1016/j.compfluid.2018.12.010},
journal = {Computers and Fluids},
issn = {0045-7930},
number = ,
volume = 183,
place = {United States},
year = {2018},
month = {12}
}

Journal Article:
Free Publicly Available Full Text
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