10 papers
Numerical Realization of an Entropy-Based Selection Principle in the Example of Kelvin-Helmholtz Instability
Shaoshuai Chu, Michael Herty
In this paper, we extend numerical schemes based on parameterized Young measures and linear programming to two space dimensions and apply them to the Kelvin-Helmholtz instability g…
Entropy-Based Local Characteristic Decomposition
Shaoshuai Chu, Michael Herty, Alexander Kurganov
Local characteristic decomposition (LCD) is widely used in high-order numerical methods for hyperbolic systems of conservation laws to reduce spurious oscillations appearing in the…
New Scheme Adaption Strategy for Hyperbolic Conservation Laws
Shaoshuai Chu, Michael Herty, Alexander Kurganov
We introduce a new scheme adaption strategy for one- and two-dimensional hyperbolic systems of conservation laws. The proposed approach builds upon the adaptive framework introduce…
A Comparative Study of Low-Dissipation Numerical Schemes for Hyperbolic Conservation Laws
Shaoshuai Chu, Michael Herty
This work provides a comparative assessment of several low-dissipation numerical schemes for hyperbolic conservation laws, highlighting their performance relative to the classical…
A Bayesian Approach to Feedback Control for Hyperbolic Balance Laws
Markus Bambach, Shaoshuai Chu, Michael Herty +1
We propose a Bayesian framework for feedback boundary control of hyperbolic balance laws. The method propagates a probability distribution over feedback parameters using Lyapunov d…
Numerical Study of Dissipative Weak Solutions for the Euler Equations of Gas Dynamics
Shaoshuai Chu, Michael Herty, Alexander Kurganov +2
We study dissipative weak (DW) solutions of the Euler equations of gas dynamics using the first-, second-, third-, fifth-, seventh-, and ninth-order local characteristic decomposit…
High-Order Schemes for Hyperbolic Conservation Laws Using Young Measures
Shaoshuai Chu, Michael Herty
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-…
Numerical Analysis of Stabilization for Random Hyperbolic Systems of Conservation Laws
Shaoshuai Chu, Michael Herty, Alexander Kurganov
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and in…
High-Order Flux Splitting Schemes for the Euler Equations of Gas Dynamics
Shaoshuai Chu, Michael Herty, Eleuterio F. Toro
We develop high-order flux splitting schemes for the one- and two-dimensional Euler equations of gas dynamics. The proposed schemes are high-order extensions of the existing first-…
Solving Random Hyperbolic Conservation Laws Using Linear Programming
Shaoshuai Chu, Michael Herty, Maria Lukacova-Medvidova +1
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutio…