4 citations · 6 across the 11 of their papers we have counts for
7 papers · 1 filter
Turnpike property for hierarchical optimal control problems: from particle systems to hydrodynamic equations
Michael Herty, Yizhou Zhou
This work is concerned with a hierarchical framework of optimal control problems connecting interacting particle systems, the mean field limit equations, and associated hydrodynami…
Numerical Study of Random Kelvin-Helmholtz Instability
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solu…
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-…
High-dimensional stochastic finite volumes using the tensor train format
Juliette Dubois, Michael Herty, Siegfried Müller
A method for the uncertainty quantification of nonlinear hyperbolic conservation laws with many uncertain parameters is presented. The method combines stochastic finite volume meth…
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…