5 papers
TVD and TVB preservation without TVD time discretization for discontinuous Galerkin methods
Ziyao Xu, Zheng Sun
Total variation diminishing (TVD) and total variation bounded (TVB) properties are crucial for controlling spurious oscillations in numerical solutions of conservation laws. In the…
A limiter-based approach to construct high-order fully-discrete entropy stable explicit DG schemes for hyperbolic conservation laws
Yuchang Liu, Wei Guo, Yan Jiang +1
This paper presents a class of novel high-order fully-discrete entropy stable (ES) discontinuous Galerkin (DG) schemes with explicit time discretization. The proposed methodology e…
A bound-preserving Runge--Kutta discontinuous Galerkin method with compact stencils for hyperbolic conservation laws
Chen Liu, Zheng Sun, Xiangxiong Zhang
In this paper, we develop bound-preserving techniques for the Runge--Kutta (RK) discontinuous Galerkin (DG) method with compact stencils (cRKDG method) for hyperbolic conservation…
Stability and Time-Step Constraints of Exponential Time Differencing Runge--Kutta Discontinuous Galerkin Methods for Advection-Diffusion Equations
Ziyao Xu, Zheng Sun, Yong-Tao Zhang
In this paper, we investigate the stability and time-step constraints for solving advection-diffusion equations using exponential time differencing (ETD) Runge-Kutta (RK) methods i…
Reducing polynomial degree by one for inner-stage operators affects neither stability type nor accuracy order of the Runge--Kutta discontinuous Galerkin method
Zheng Sun
The Runge--Kutta (RK) discontinuous Galerkin (DG) method is a mainstream numerical algorithm for solving hyperbolic equations. In this paper, we use the linear advection equation i…