NDLI: Immersed Boundary Method for Variable Viscosity and Variable Density Problems Using Fast Constant-Coefficient Linear Solvers II: Theory

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Fai, Thomas G. Mori, Yoichiro Peskin, Charles S. Griffith, Boyce E.
Copyright Year	2014
Abstract	We analyze the stability and convergence of first-order accurate and second-order accurate timestepping schemes for the Navier--Stokes equations with variable viscosity. These schemes are characterized by a mixed implicit/explicit treatment of the viscous term, in which a numerical parameter, $\lambda$, determines the degree of splitting between the implicit and explicit contributions. The reason for this splitting is that it avoids the need to solve computationally expensive linear systems that may change at each timestep. Provided the parameter $\lambda$ is within a permissible range, we prove that the first-order accurate and second-order accurate schemes are convergent. We show further that the efficiency of the second-order accurate scheme depends on how $\lambda$ is chosen within the permissible range, and we discuss choices that work well in practice. We use parameters motivated by this analysis to simulate internal gravity waves, which arise in stratified fluids with variable density. We examine how the wave properties change in the nonlinear and variable viscosity regime, and we test how well our theory predicts the speed of convergence of the iteration used in the second-order accurate timestepping scheme. (An erratum is attached.)
Starting Page	B589
Ending Page	B621
Page Count	33
File Format	PDF
ISSN	10648275
DOI	10.1137/12090304X
e-ISSN	10957197
Issue Number	3
Volume Number	36
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2014-06-17
Access Restriction	Subscribed
Subject Keyword	Stability and convergence of numerical methods variable viscosity incompressible flow convergence immersed boundary method Stokes and related (Oseen, etc.) flows stability Finite difference methods
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics 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