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

Brady, Peter T.; Livescu, Daniel

doi:10.1016/j.compfluid.2018.12.010

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

Journal Article · Wed Dec 26 23:00:00 EST 2018 · Computers and Fluids

DOI:https://doi.org/10.1016/j.compfluid.2018.12.010· OSTI ID:1493552

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Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

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.

View Accepted Manuscript (DOE)

Research Organization:: Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: 89233218CNA000001

OSTI ID:: 1493552

Report Number(s):: LA-UR--17-21169

Journal Information:: Computers and Fluids, Journal Name: Computers and Fluids Vol. 183; ISSN 0045-7930

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (19)

The Stability of Numerical Boundary Treatments for Compact High-Order Finite-Difference Schemes Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul Journal of Computational Physics, Vol. 108, Issue 2 https://doi.org/10.1006/jcph.1993.1182	journal	October 1993
Time-Stable Boundary Conditions for Finite-Difference Schemes Solving Hyperbolic Systems: Methodology and Application to High-Order Compact Schemes Carpenter, Mark H.; Gottlieb, David; Abarbanel, Saul Journal of Computational Physics, Vol. 111, Issue 2 https://doi.org/10.1006/jcph.1994.1057	journal	April 1994
Direct Numerical Simulation of a Turbulent Reactive Plume on a Parallel Computer Cook, Andrew W.; Riley, James J. Journal of Computational Physics, Vol. 129, Issue 2 https://doi.org/10.1006/jcph.1996.0249	journal	December 1996
Low-Dissipative High-Order Shock-Capturing Methods Using Characteristic-Based Filters Yee, H. C.; Sandham, N. D.; Djomehri, M. J. Journal of Computational Physics, Vol. 150, Issue 1 https://doi.org/10.1006/jcph.1998.6177	journal	March 1999
Strict Stability of High-Order Compact Implicit Finite-Difference Schemes: The Role of Boundary Conditions for Hyperbolic PDEs, II Abarbanel, Saul S.; Chertock, Alina E.; Yefet, Amir Journal of Computational Physics, Vol. 160, Issue 1 https://doi.org/10.1006/jcph.2000.6421	journal	May 2000
On the Use of Higher-Order Finite-Difference Schemes on Curvilinear and Deforming Meshes Visbal, Miguel R.; Gaitonde, Datta V. Journal of Computational Physics, Vol. 181, Issue 1 https://doi.org/10.1006/jcph.2002.7117	journal	September 2002
Compact finite difference schemes with spectral-like resolution Lele, Sanjiva K. Journal of Computational Physics, Vol. 103, Issue 1 https://doi.org/10.1016/0021-9991(92)90324-R	journal	November 1992
A robust high-order compact method for large eddy simulation Nagarajan, Santhanam; Lele, Sanjiva K.; Ferziger, Joel H. Journal of Computational Physics, Vol. 191, Issue 2 https://doi.org/10.1016/S0021-9991(03)00322-X	journal	November 2003
Improving the boundary efficiency of a compact finite difference scheme through optimising its composite template Turner, Jacob M.; Haeri, Sina; Kim, Jae Wook Computers & Fluids, Vol. 138 https://doi.org/10.1016/j.compfluid.2016.08.007	journal	October 2016
Grid stabilization of high-order one-sided differencing I: First-order hyperbolic systems Hagstrom, Thomas; Hagstrom, George Journal of Computational Physics, Vol. 223, Issue 1 https://doi.org/10.1016/j.jcp.2006.09.017	journal	April 2007
Optimised boundary compact finite difference schemes for computational aeroacoustics Kim, Jae Wook Journal of Computational Physics, Vol. 225, Issue 1 https://doi.org/10.1016/j.jcp.2007.01.008	journal	July 2007
Transition stages of Rayleigh–Taylor instability between miscible fluids Cook, Andrew W.; Dimotakis, Paul E. Journal of Fluid Mechanics, Vol. 443 https://doi.org/10.1017/S0022112001005377	journal	September 2001
Turbulence structure behind the shock in canonical shock–vortical turbulence interaction Ryu, Jaiyoung; Livescu, Daniel Journal of Fluid Mechanics, Vol. 756 https://doi.org/10.1017/jfm.2014.477	journal	September 2014
Numerical study of variable density turbulence interaction with a normal shock wave Tian, Yifeng; Jaberi, Farhad A.; Li, Zhaorui Journal of Fluid Mechanics, Vol. 829 https://doi.org/10.1017/jfm.2017.542	journal	September 2017
Artificial fluid properties for large-eddy simulation of compressible turbulent mixing Cook, Andrew W. Physics of Fluids, Vol. 19, Issue 5 https://doi.org/10.1063/1.2728937	journal	May 2007
The convergence rate for difference approximations to mixed initial boundary value problems Gustafsson, Bertil Mathematics of Computation, Vol. 29, Issue 130 https://doi.org/10.1090/S0025-5718-1975-0386296-7	journal	May 1975
Discrete Conservation Properties of Unstructured Mesh Schemes Perot, J. Blair Annual Review of Fluid Mechanics, Vol. 43, Issue 1 https://doi.org/10.1146/annurev-fluid-122109-160645	journal	January 2011
M ODELING A RTIFICIAL B OUNDARY C ONDITIONS FOR C OMPRESSIBLE F LOW Colonius, Tim Annual Review of Fluid Mechanics, Vol. 36, Issue 1 https://doi.org/10.1146/annurev.fluid.36.050802.121930	journal	January 2004
High-Resolution Numerical Method for Supercritical Flows with Large Density Variations Terashima, Hiroshi; Kawai, Soshi; Yamanishi, Nobuhiro AIAA Journal, Vol. 49, Issue 12 https://doi.org/10.2514/1.J051079	journal	December 2011

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97 MATHEMATICS AND COMPUTING
boundaries
conservative
finite difference
high-order
hyperbolic
non-linear
optimization
stability

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

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References (19)

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