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Mesh-Based Filtering to Alleviate Time-Step Restrictions in Runge--Kutta Discontinuous Galerkin Methods in Spherical-polar Coordinates: Application to the Euler Equations
Joseph Hunter, Eirik Endeve, Yulong Xing
We propose a mesh-based filtering approach to alleviate the severe timestep restrictions arising in explicit Runge--Kutta discontinuous Galerkin (RKDG) methods formulated in spheri…
Realizability-Preserving Discontinuous Galerkin Method for Spectral Two-Moment Radiation Transport in Special Relativity
Joseph Hunter, Eirik Endeve, M. Paul Laiu +1
We present a realizability-preserving numerical method for solving a spectral two-moment model to simulate the transport of massless, neutral particles interacting with a steady ba…
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…