11 papers
Limiter-based fully-discrete entropy stable explicit DG schemes for ideal MHD equations
Yuchang Liu, Yan Jiang, Zheng Sun
We propose a class of high-order fully-discrete entropy stable (ES) explicit discontinuous Galerkin (DG) solvers for the compressible ideal magnetohydrodynamics (MHD) equations. Ou…
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…
Structure-preserving nodal DG method for the Euler equations with gravity: well-balanced, entropy stable, and positivity preserving
Yuchang Liu, Wei Guo, Yan Jiang +1
We propose an entropy stable and positivity preserving discontinuous Galerkin (DG) scheme for the Euler equations with gravity, which is also well-balanced for hydrostatic equilibr…
A globally divergence-free entropy stable nodal DG method for conservative ideal MHD equations
Yuchang Liu, Wei Guo, Yan Jiang +1
We propose an arbitrarily high-order globally divergence-free entropy stable nodal discontinuous Galerkin (DG) method to directly solve the conservative form of the ideal MHD equat…
Non-oscillatory entropy stable DG schemes for hyperbolic conservation law
Yuchang Liu, Wei Guo, Yan Jiang +1
In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific…
A new type of simplified inverse Lax-Wendroff boundary treatment I: hyperbolic conservation laws
Shihao Liu, Tingting Li, Ziqiang Cheng +3
In this paper, we design a new kind of high order inverse Lax-Wendroff (ILW) boundary treatment for solving hyperbolic conservation laws with finite difference method on a Cartesia…