18 citations · 21 across the 5 of their papers we have counts for
5 papers
New Asymptotic Preserving, Hybrid Discontinuous Galerkin Methods the Radiation Transport Equation with Isotropic Scattering and Diffusive Scaling
Cory D. Hauck, Qiwei Sheng, Yulong Xing
Discontinuous Galerkin (DG) methods are widely adopted to discretize the radiation transport equation (RTE) with diffusive scalings. One of the most important advantages of the DG…
The Runge--Kutta discontinuous Galerkin method with stage-dependent polynomial spaces for hyperbolic conservation laws
Qifan Chen, Zheng Sun, Yulong Xing
In this paper, we present a novel class of high-order Runge--Kutta (RK) discontinuous Galerkin (DG) schemes for hyperbolic conservation laws. The new method extends beyond the trad…
Numerical analysis of a spherical harmonic discontinuous Galerkin method for scaled radiative transfer equations with isotropic scattering
Qiwei Sheng, Cory Hauck, Yulong Xing
In highly diffusion regimes when the mean free path tends to zero, the radiative transfer equation has an asymptotic behavior which is governed by a diffusion equatio…
On a numerical artifact of solving shallow water equations with a discontinuous bottom: Analysis and a nontransonic fix
Zheng Sun, Yulong Xing
In this paper, we study a numerical artifact of solving the nonlinear shallow water equations with a discontinuous bottom topography. For various first-order schemes, the numerical…
Bound-Preserving Discontinuous Galerkin Methods for Conservative Phase Space Advection in Curvilinear Coordinates
Eirik Endeve, Cory D. Hauck, Yulong Xing +1
We extend the positivity-preserving method of Zhang & Shu (2010, JCP, 229, 3091-3120) to simulate the advection of neutral particles in phase space using curvilinear coordinates. T…