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Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms

Juntao Huang Chi-Wang Shu Brown University

Numerical Analysis and Scientific Computing mathscidoc:1804.25029

Journal of Computational Physics, 361, 111-135, 2018
In this paper, we develop bound-preserving modified exponential Runge-Kutta (RK) discontinuous Galerkin (DG) schemes to solve scalar hyperbolic equations with stiff source terms by extending the idea in Zhang and Shu \cite{ZhSh:10max}. Exponential strong stability preserving (SSP) high order time discretizations are constructed and then modified to overcome the stiffness and preserve the bound of the numerical solutions. It is also straightforward to extend the method to two dimensions on rectangular and triangular meshes. Even though we only discuss the bound-preserving limiter for DG schemes, it can also be applied to high order finite volume schemes, such as weighted essentially non-oscillatory (WENO) finite volume schemes as well.
Discontinuous Galerkin method; finite volume scheme; scalar hyperbolic equations; stiff source; bound-preserving scheme; high order accuracy; exponential Runge-Kutta method
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@inproceedings{juntao2018bound-preserving,
  title={Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms},
  author={Juntao Huang, and Chi-Wang Shu},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416110611834827064},
  booktitle={Journal of Computational Physics},
  volume={361},
  pages={111-135},
  year={2018},
}
Juntao Huang, and Chi-Wang Shu. Bound-preserving modified exponential Runge-Kutta discontinuous Galerkin methods for scalar hyperbolic equations with stiff source terms. 2018. Vol. 361. In Journal of Computational Physics. pp.111-135. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180416110611834827064.
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