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Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids

Kramer, R. M. J. and Pantano, C. and Pullin, D. I. (2009) Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids. Journal of Computational Physics, 228 (14). pp. 5280-5297. ISSN 0021-9991. https://resolver.caltech.edu/CaltechAUTHORS:20090904-101804788

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Abstract

A class of finite-difference interface schemes suitable for two-dimensional cell-centered grids with patch-refinement and step-changes in resolution is presented. Grids of this type are generated by adaptive mesh refinement methods according to resolution needs dictated by the physics of the problem being modeled. For these grids, coarse and fine nodes are not aligned at the mesh interfaces, resulting in hanging nodes. Three distinct geometries are identified at the interfaces of a domain with interior patch-refinement: edges, concave corners and convex corners. Asymptotic stability in time of the numerical scheme is achieved by imposing a summation-by-parts condition on the interface closure, which is thus also nondissipative. Interface stencils corresponding to an explicit fourth-order finite-difference scheme are presented for each geometry. To preserve stability, a reduction in local accuracy is required at the corner geometries. It is also found that no second-order accurate solution exists that satisfies the summation-by-parts condition. Tests using the 2-D scalar advection equation and an inviscid compressible vortex support the stability and accuracy of these stencils for both linear and nonlinear problems.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1016/j.jcp.2009.04.010DOIUNSPECIFIED
Additional Information:Copyright © 2009 Elsevier. Received 27 May 2008; revised 3 April 2009; accepted 8 April 2009. Available online 22 April 2009. This work was supported by the ASC program of the Department of Energy under Subcontract No. B341492 of DOE Contract W-7405-ENG-48. The authors would like to thank the reviewers for valuable and constructive comments, in particular for requesting clarifications with respect to discrete conservation. Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.jcp.2009.04.010.
Group:GALCIT
Funders:
Funding AgencyGrant Number
Department of EnergyW-7405-ENG-48
Subject Keywords:High-order finite difference; Mesh interface; Stable stencil; Adaptive mesh refinement; Summation by parts
Issue or Number:14
Record Number:CaltechAUTHORS:20090904-101804788
Persistent URL:https://resolver.caltech.edu/CaltechAUTHORS:20090904-101804788
Official Citation:R.M.J. Kramer, C. Pantano, D.I. Pullin, Nondissipative and energy-stable high-order finite-difference interface schemes for 2-D patch-refined grids, Journal of Computational Physics, Volume 228, Issue 14, 1 August 2009, Pages 5280-5297, ISSN 0021-9991, DOI: 10.1016/j.jcp.2009.04.010. (http://www.sciencedirect.com/science/article/B6WHY-4W4CWVF-6/2/2f216095a8bb9461b9d02f2a785901bb)
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:15608
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:22 Sep 2009 17:59
Last Modified:03 Oct 2019 01:00

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