20 citations · 21 across the 17 of their papers we have counts for
17 papers
Invariant domain preservation for hybrid point-value and cell-average discretizations of hyperbolic equations on general meshes
Shengrong Ding, Shumo Cui, Remi Abgrall +1
This paper presents a unified invariant-domain-preserving (IDP) framework for hybrid discretizations of hyperbolic conservation laws, including active flux and PAMPA methods, in wh…
High-order fully discrete multi-entropy-stable and bound-preserving schemes for relativistic Euler equations
Linfeng Xu, Kailiang Wu
A discrete entropy inequality is the principal nonlinear stability estimate available for systems of conservation laws, and evaluating it presupposes a physically admissible state.…
GQL-Based Physical-Constraint-Preserving High-Order Finite Difference Schemes for Special Relativistic Hydrodynamics in Arbitrary Dimensions
Linfeng Xu, Shengrong Ding, Kailiang Wu
High-order accurate simulations of special relativistic hydrodynamics (RHD) are prone to numerical breakdown if intrinsic physical constraints (positive rest-mass density/pressure…
EPO: A Unified Framework for Entropy Stability, Positivity, and Oscillation Suppression
Kailiang Wu
High-order finite volume and discontinuous Galerkin methods are often stabilized by separate nonlinear devices for admissibility, entropy control, and oscillation suppression. This…
High Order Numerical Methods Preserving Invariant Domain for Hyperbolic and Related Systems
Kailiang Wu, Xiangxiong Zhang, Chi-Wang Shu
Admissible states in hyperbolic systems and related equations often form a convex invariant domain. Numerical violations of this domain can lead to loss of hyperbolicity, resulting…
Bound-Preserving WENO Schemes for Temple-class systems
Wei Chen, Shumo Cui, Kailiang Wu +2
This paper explores numerical schemes for Temple-class systems, which are integral to various applications including one-dimensional two-phase flow, elasticity, traffic flow, and s…
Oscillation-eliminating central DG schemes for hyperbolic conservation laws
Manting Peng, Kailiang Wu, Caiyou Yuan
This paper proposes and analyzes a class of essentially non-oscillatory central discontinuous Galerkin (CDG) methods for general hyperbolic conservation laws. First, we introduce a…
On Local Minimum Entropy Principle of High-Order Schemes for Relativistic Euler Equations
Shumo Cui, Kailiang Wu, Linfeng Xu
This paper establishes the minimum entropy principle (MEP) for the relativistic Euler equations with a broad class of equations of state (EOSs) and addresses the challenge of prese…
Bound-preserving OEDG schemes for Aw-Rascle-Zhang traffic models on networks
Wei Chen, Shumo Cui, Kailiang Wu +1
Physical solutions to the widely used Aw-Rascle-Zhang (ARZ) traffic model and the adapted pressure (AP) ARZ model should satisfy the positivity of density, the minimum and maximum…
High-order Accurate Entropy Stable Schemes for Relativistic Hydrodynamics with General Synge-type Equation of State
Linfeng Xu, Shengrong Ding, Kailiang Wu
All the existing entropy stable (ES) schemes for relativistic hydrodynamics (RHD) in the literature were restricted to the ideal equation of state (EOS), which however is often a p…
Spectral Volume from a DG perspective: Oscillation Elimination, Stability, and Optimal Error Estimates
Zhuoyun Li, Kailiang Wu
The discontinuous Galerkin (DG) method and the spectral volume (SV) method are two widely-used numerical methodologies for solving hyperbolic conservation laws. In this paper, we d…
High-Order Oscillation-Eliminating Hermite WENO Method for Hyperbolic Conservation Laws
Chuan Fan, Kailiang Wu
This paper proposes high-order accurate, oscillation-eliminating Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws. The…
Robust DG Schemes on Unstructured Triangular Meshes: Oscillation Elimination and Bound Preservation via Optimal Convex Decomposition
Shengrong Ding, Shumo Cui, Kailiang Wu
Discontinuous Galerkin (DG) schemes on unstructured meshes offer the advantages of compactness and the ability to handle complex computational domains. However, their robustness an…
Structure-Preserving Oscillation-Eliminating Discontinuous Galerkin Schemes for Ideal MHD Equations: Locally Divergence-Free and Positivity-Preserving
Mengqing Liu, Kailiang Wu
Numerically simulating magnetohydrodynamics (MHD) poses notable challenges, including the suppression of spurious oscillations near discontinuities (e.g., shocks) and preservation…
Bound-Preserving Framework for Central-Upwind Schemes for General Hyperbolic Conservation Laws
Shumo Cui, Alexander Kurganov, Kailiang Wu
Central-upwind (CU) schemes are Riemann-problem-solver-free finite-volume methods widely applied to a variety of hyperbolic systems of PDEs. Exact solutions of these systems typica…
GQL-Based Bound-Preserving and Locally Divergence-Free Central Discontinuous Galerkin Schemes for Relativistic Magnetohydrodynamics
Shengrong Ding, Kailiang Wu
This paper develops novel and robust central discontinuous Galerkin (CDG) schemes of arbitrarily high-order accuracy for special relativistic magnetohydrodynamics (RMHD) with a gen…
OEDG: Oscillation-eliminating discontinuous Galerkin method for hyperbolic conservation laws
Manting Peng, Zheng Sun, Kailiang Wu
Controlling spurious oscillations is crucial for designing reliable numerical schemes for hyperbolic conservation laws. This paper proposes a novel, robust, and efficient oscillati…