NDLI: Error estimators for the position of discontinuities in hyperbolic conservation laws with source terms which are solved using operator splitting

Content Provider	Springer Nature Link
Author	Jeltsch, R. Klingenstein, P.
Copyright Year	1999
Abstract	When computing numerical solutions of hyperbolic conservation laws with source terms, one may obtain spurious solutions — these are unphysical solutions that only occur in numerics such as shock waves moving with wrong speeds, cf. [9], [3], [1], [13], [4]. Therefore it is important to know how errors of the location of a discontinuity can be controlled. To derive appropriate error-estimates and to use them to control such errors, is the aim of our investigations in this paper. We restrict our considerations to numerical solutions which are computed by using a splitting method. In splitting methods, the homogeneous conservation law and an ordinary differential equation (modelling the source term) are solved separately in each time step. Firstly, we derive error-estimates for the scalar Riemann problem. The analysis shows that the local error of the location of a discontinuity mainly consists of two parts. The first part is introduced by the splitting and the second part is due to smearing of the discontinuity. Next, these error-estimates are used to construct an adaptation of the step size so that the error of the location of the discontinuity remains sufficiently small. The adaptation is applied to several examples, which are a scalar problem, a simplified combustion model, and the one-dimensional inviscid reacting compressible Euler equations. All the examples show that the adaptation based on the derived error-estimates works well. The theory can also be extended to planar two-dimensional problems.
Starting Page	231
Ending Page	249
Page Count	19
File Format	PDF
ISSN	14329360
Journal	Computing and Visualization in Science
Volume Number	1
Issue Number	4
Language	English
Publisher	Springer-Verlag
Publisher Date	1999-07-01
Publisher Place	Berlin, Heidelberg
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article
Subject	Theoretical Computer Science Engineering Computational Theory and Mathematics Computer Vision and Pattern Recognition Modeling and Simulation Software

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in