@Article{CiCP-35-2,
author = {Liu, Lele and Zhang, Hong and Xu, Qian and Songhe, Song},
title = {Maximum-Principle-Preserving, Steady-State-Preserving and Large Time-Stepping High-Order Schemes for Scalar Hyperbolic Equations with Source Terms},
journal = {Communications in Computational Physics},
year = {2024},
volume = {35},
number = {2},
pages = {498--523},
abstract = {<p style="text-align: justify;">In this paper, we construct a family of temporal high-order parametric relaxation Runge–Kutta (pRRK) schemes for stiff ordinary differential equations (ODEs), and explore their application in solving hyperbolic conservation laws
with source terms. The new time discretization methods are explicit, large time-stepping, delay-free and able to preserve steady state. They are combined with
fifth-order weighted compact nonlinear schemes (WCNS5) spatial discretization and
parametrized maximum-principle-preserving (MPP) flux limiters to solve scalar hyperbolic equations with source terms. We prove that the fully discrete schemes preserve the maximum principle strictly. Through benchmark test problems, we demonstrate that the proposed schemes have fifth-order accuracy in space, fourth-order accuracy in time and allow for large time-stepping without time delay. Both theoretical
analyses and numerical experiments are presented to validate the benefits of the proposed schemes.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2023-0143},
url = {https://global-sci.com/article/90931/maximum-principle-preserving-steady-state-preserving-and-large-time-stepping-high-order-schemes-for-scalar-hyperbolic-equations-with-source-terms}
}