NDLI: High Order Maximum Principle Preserving Finite Volume Method for Convection Dominated Problems

Content Provider	Springer Nature Link
Author	Yang, Pei Xiong, Tao Qiu, Jing Mei Xu, Zhengfu
Copyright Year	2015
Abstract	In this paper, we investigate the application of the maximum principle preserving (MPP) parameterized flux limiters to the high order finite volume scheme with Runge–Kutta time discretization for solving convection dominated problems. Such flux limiter was originally proposed in Xu (Math Comput 83:2213–2238, 2014) and further developed in Xiong et al. (J Comput Phys 252:310–331, 2013) for finite difference WENO schemes with Runge–Kutta time discretization for convection equations. The main idea is to limit the temporal integrated high order numerical flux toward a first order MPP monotone flux. In this paper, we generalize such flux limiter to high order finite volume methods solving convection-dominated problems, which is easy to implement and introduces little computational overhead. More importantly, for the first time in the finite volume setting, we provide a general proof that the proposed flux limiter maintains high order accuracy of the original WENO scheme for linear advection problems without any additional time step restriction. For general nonlinear convection-dominated problems, we prove that the proposed flux limiter introduces up to $${\mathcal {O}}({\varDelta x^3} + \varDelta t^3)$$ modification to the high order temporal integrated flux in the original WENO scheme without extra time step constraint. We also numerically investigate the preservation of up to ninth order accuracy of the proposed flux limiter in a general setting. The advantage of the proposed method is demonstrated through various numerical experiments.
Starting Page	795
Ending Page	820
Page Count	26
File Format	PDF
ISSN	08857474
Journal	Journal of Scientific Computing
Volume Number	67
Issue Number	2
e-ISSN	15737691
Language	English
Publisher	Springer US
Publisher Date	2015-09-19
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Convection–diffusion equation High order WENO scheme Finite volume method Maximum principle preserving Flux limiters Algorithms Computational Mathematics and Numerical Analysis ApplicationMathematics/Computational Methods of Engineering Theoretical, Mathematical and Computational Physics
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Theoretical Computer Science Engineering Computational Theory and Mathematics Computational Mathematics Numerical Analysis 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

Parametrized Maximum Principle Preserving Limiter for Finite Difference WENO Schemes Solving Convection-Dominated Diffusion Equations

Parametrized Maximum Principle Preserving Flux Limiters for High Order Schemes Solving Multi-Dimensional Scalar Hyperbolic Conservation Laws

Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

High order maximum principle preserving finite volume method for convection dominated problems

High order maximum principle preserving finite volume method for convection dominated problems

High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations

A Maximum-Principle-Satisfying High-Order Finite Volume Compact WENO Scheme for Scalar Conservation Laws with Applications in Incompressible Flows

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Scalar Convection Diffusion Equations

High Order Maximum Principle Preserving Finite Volume Method for Convection Dominated Problems

Similar Documents

Parametrized Maximum Principle Preserving Limiter for Finite Difference WENO Schemes Solving Convection-Dominated Diffusion Equations

Parametrized Maximum Principle Preserving Flux Limiters for High Order Schemes Solving Multi-Dimensional Scalar Hyperbolic Conservation Laws

Parametrized Positivity Preserving Flux Limiters for the High Order Finite Difference WENO Scheme Solving Compressible Euler Equations

High order maximum principle preserving finite volume method for convection dominated problems

High order maximum principle preserving finite volume method for convection dominated problems

High Order Maximum-Principle-Preserving Discontinuous Galerkin Method for Convection-Diffusion Equations

A Maximum-Principle-Satisfying High-Order Finite Volume Compact WENO Scheme for Scalar Conservation Laws with Applications in Incompressible Flows

Maximum-Principle-Satisfying and Positivity-Preserving High Order Discontinuous Galerkin Schemes for Conservation Laws on Triangular Meshes

A High Order Accurate Bound-Preserving Compact Finite Difference Scheme for Scalar Convection Diffusion Equations

High Order Maximum Principle Preserving Finite Volume Method for Convection Dominated Problems