NDLI: Composite Schemes for Conservation Laws

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Liska, Richard Wendroff, Burton
Copyright Year	1998
Abstract	Global composition of several time steps of the two-step Lax--Wendroff scheme followed by a Lax--Friedrichs step seems to enhance the best features of both, although it is only first order accurate. We show this by means of some examples of one-dimensional shallow water flow over an obstacle. In two dimensions we present a new version of Lax--Friedrichs and an associated second order predictor-corrector method. Composition of these schemes is shown to be effective and efficient for some two-dimensional Riemann problems and for Noh's infinite strength cylindrical shock problem. We also show comparable results for composition of the predictor-corrector scheme with a modified second order accurate weighted essentially nonoscillatory (WENO) scheme. That composition is second order but is more efficient and has better symmetry properties than WENO alone. For scalar advection in two dimensions the optimal stability of the new predictor-corrector scheme is shown using computer algebra. We also show that the generalization of this scheme to three dimensions is unstable, but by using sampling we are able to show that the composites are suboptimally stable.
Starting Page	2250
Ending Page	2271
Page Count	22
File Format	PDF
ISSN	00361429
DOI	10.1137/S0036142996310976
e-ISSN	10957170
Issue Number	6
Volume Number	35
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2006-07-25
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods Conservation laws composite schemes conservation laws Lax--Wendroff scheme Lax--Friedrichs scheme hyperbolic systems two-dimensional Riemann problem Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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