papers

Publications (11)

math.NA2024

A Hybrid Finite-Difference-Particle Method for Chemotaxis Models

Alina Chertock, Shumo Cui, Alexander Kurganov +1

Chemotaxis systems play a crucial role in modeling the dynamics of bacterial and cellular behaviors, including propagation, aggregation, and pattern formation, all under the influe…

math.NA2024

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…

math.NA2025

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…

math.NA2022

A Diffuse-Domain Based Numerical Method for a Chemotaxis-Fluid Model

Chenxi Wang, Alina Chertock, Shumo Cui +2

In this paper, we consider a coupled chemotaxis-fluid system that models self-organized collective behavior of oxytactic bacteria in a sessile drop. This model describes the biolog…

math.NA2024

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…

math.NA2017

Well-Balanced Schemes for the Euler Equations with Gravitation: Conservative Formulation Using Global Fluxes

Alina Chertock, Shumo Cui, Alexander Kurganov +2

We develop a second-order well-balanced central-upwind scheme for the compressible Euler equations with gravitational source term. Here, we advocate a new paradigm based on a purel…

math.NA2022

Is the Classic Convex Decomposition Optimal for Bound-Preserving Schemes in Multiple Dimensions?

Shumo Cui, Shengrong Ding, Kailiang Wu

Since proposed in [X. Zhang and C.-W. Shu, J. Comput. Phys., 229: 3091--3120, 2010], the Zhang--Shu framework has attracted extensive attention and motivated many bound-preserving…

eess.SY2017

Dissipation of stop-and-go waves via control of autonomous vehicles: Field experiments

Raphael E. Stern, Shumo Cui, Maria Laura Delle Monache +11

Traffic waves are phenomena that emerge when the vehicular density exceeds a critical threshold. Considering the presence of increasingly automated vehicles in the traffic stream,…

math.NA2022

On Optimal Cell Average Decomposition for High-Order Bound-Preserving Schemes of Hyperbolic Conservation Laws

Shumo Cui, Shengrong Ding, Kailiang Wu

This paper presents the first systematic study on the fundamental problem of seeking optimal cell average decomposition (OCAD), which arises from constructing efficient high-order…

math.NA2024

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…

math.NA2025

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…