Universität zu Köln

Friedrich, Lucas, Fernandez, David C. Del Rey, Winters, Andrew R., Gassner, Gregor J., Zingg, David W. and Hicken, Jason (2018). Conservative and Stable Degree Preserving SBP Operators for Non-conforming Meshes. J. Sci. Comput., 75 (2). S. 657 - 687. NEW YORK: SPRINGER/PLENUM PUBLISHERS. ISSN 1573-7691

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Abstract

Non-conforming numerical approximations offer increased flexibility for applications that require high resolution in a localized area of the computational domain or near complex geometries. Two key properties for non-conforming methods to be applicable to real world applications are conservation and energy stability. The summation-by-parts (SBP) property, which certain finite-difference and discontinuous Galerkin methods have, finds success for the numerical approximation of hyperbolic conservation laws, because the proofs of energy stability and conservation can discretely mimic the continuous analysis of partial differential equations. In addition, SBP methods can be developed with high-order accuracy, which is useful for simulations that contain multiple spatial and temporal scales. However, existing non-conforming SBP schemes result in a reduction of the overall degree of the scheme, which leads to a reduction in the order of the solution error. This loss of degree is due to the particular interface coupling through a simultaneous-approximation-term (SAT). We present in this work a novel class of SBP-SAT operators that maintain conservation, energy stability, and have no loss of the degree of the scheme for non-conforming approximations. The new degree preserving discretizations require an ansatz that the norm matrix of the SBP operator is of a degree , in contrast to, for example, existing finite difference SBP operators, where the norm matrix is accurate. We demonstrate the fundamental properties of the new scheme with rigorous mathematical analysis as well as numerical verification.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Friedrich, Lucas UNSPECIFIED UNSPECIFIED UNSPECIFIED Fernandez, David C. Del Rey UNSPECIFIED UNSPECIFIED UNSPECIFIED Winters, Andrew R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Gassner, Gregor J. UNSPECIFIED UNSPECIFIED UNSPECIFIED Zingg, David W. UNSPECIFIED UNSPECIFIED UNSPECIFIED Hicken, Jason UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-188894
DOI:	10.1007/s10915-017-0563-z
Journal or Publication Title:	J. Sci. Comput.
Volume:	75
Number:	2
Page Range:	S. 657 - 687
Date:	2018
Publisher:	SPRINGER/PLENUM PUBLISHERS
Place of Publication:	NEW YORK
ISSN:	1573-7691
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language BY-PARTS OPERATORS; FINITE-DIFFERENCE METHODS; NAVIER-STOKES EQUATIONS; BOUNDARY-CONDITIONS; SUMMATION; ORDER; SCHEMES; QUADRATURE; ACCURACY; EULER Multiple languages Mathematics, Applied Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/18889