Bound-Preserving High-Order Schemes
Document Type
Article
Publication Date
1-2017
Department
Department of Mathematical Sciences
Abstract
For the initial value problem of scalar conservation laws, a bound-preserving property is desired for numerical schemes in many applications. Traditional methods to enforce a discrete maximum principle by defining the extrema as those of grid point values in finite difference schemes or cell averages in finite volume schemes usually result in an accuracy degeneracy to second-order around smooth extrema. On the other hand, successful and popular high-order accurate schemes do not satisfy a strict bound-preserving property. We review two approaches for enforcing the bound-preserving property in high-order schemes. The first one is a general framework to design a simple and efficient limiter for finite volume and discontinuous Galerkin schemes without destroying high-order accuracy. The second one is a bound-preserving flux limiter, which can be used on high-order finite difference, finite volume and discontinuous Galerkin schemes.
Publication Title
Handbook of Numerical Analysis
Recommended Citation
Xu, Z.,
&
Zhang, X.
(2017).
Bound-Preserving High-Order Schemes.
Handbook of Numerical Analysis,
18, 81-102.
http://doi.org/10.1016/bs.hna.2016.08.002
Retrieved from: https://digitalcommons.mtu.edu/michigantech-p/5868