9 papers · 1 filter
Physics-Informed Learning of Probabilistic Gegenbauer Reconstruction for Transport-Dominated Problems
Lei Yan, Yan Jiang
Transport-dominated problems remain challenging for data-driven methods, which often exhibit severe numerical oscillations near shocks or steep gradients due to globally supported…
Weighted Inverse Lax-Wendroff Boundary Treatment of Discontinuous Galerkin Methods for Conservation Laws
Yongjie Bi, Yan Jiang, Yong Liu
In this paper, we propose a weighted inverse Lax-Wendroff (WILW) boundary treatment for the discontinuous Galerkin (DG) method on unfitted meshes to efficiently solve hyperbolic co…
Post-Processing Reduced-Order Models for Transport-Dominated Problems by Gegenbauer Reconstruction
Lei Yan, Yan Jiang, Chi-Wang Shu
In this paper, we develop a physics-based post-processing technique for data-driven reduced-order models (ROMs) of transport-dominated problems. Besides the slow decay of the Kolmo…
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…
Structure-preserving nodal DG method for Euler equations with gravity II: general equilibrium states
Yuchang Liu, Wei Guo, Yan Jiang +1
We develop an entropy-stable nodal discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced with respect to general equilibrium solution…
Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite difference HWENO methods
Guangyao Zhu, Yan Jiang, Zhuang Zhao +1
This paper presents a novel inverse Lax-Wendroff (ILW) boundary treatment for finite difference Hermite weighted essentially non-oscillatory (HWENO) schemes to solve hyperbolic con…