5 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…
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…
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…
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…