4 citations · 6 across the 11 of their papers we have counts for
21 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…
Sensitivity Calculus and its Numerical Implementation for Multi-D Hyperbolic Balance Laws
Olivia Dreßen, Michael Herty, Adrian Kolb +1
We investigate the sensitivity of solutions to multi-dimensional scalar balance laws with respect to perturbations of the initial data analytically and numerically. Reliable first-…
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…
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…
A numerical method for solving the generalized tangent vector of hyperbolic systems
Michael Herty, Yizhou Zhou
This work is concerned with the computation of the first-order variation for one-dimensional hyperbolic partial differential equations. In the case of shock waves the main challeng…
An Asymptotic-Preserving Scheme for Isentropic Flow in Pipe Networks
Michael Redle, Michael Herty
We consider the simulation of isentropic flow in pipelines and pipe networks. Standard operating conditions in pipe networks suggest an emphasis to simulate low Mach and high frict…
Numerical Boundary Control of Multi-Dimensional Hyperbolic Equations
Michael Herty, Kai Hinzmann, Siegfried Müller +1
Existing theoretical stabilization results for linear, hyperbolic multi-dimensional problems are extended to the discretized multi-dimensional problems. In contrast to existing the…
A multiscale Consensus-Based algorithm for multi-level optimization
Michael Herty, Yuyang Huang, Dante Kalise +1
A novel multiscale consensus-based optimization (CBO) algorithm for solving bi- and tri-level optimization problems is introduced. Existing CBO techniques are generalized by the pr…
Novel Local Characteristic Decomposition Based Path-Conservative Central-Upwind Schemes
Shaoshuai Chu, Michael Herty, Alexander Kurganov
We introduce local characteristic decomposition based path-conservative central-upwind schemes for (nonconservative) hyperbolic systems of balance laws. The proposed schemes are ma…
On the relation between approaches for boundary feedback control of hyperbolic systems
Michael Herty, Ferdinand Thein
Stabilization of partial differential equations is a topic of utmost importance in mathematics as well as in engineering sciences. Concerning one dimensional problems there exists…
New High-Order Numerical Methods for Hyperbolic Systems of Nonlinear PDEs with Uncertainties
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we develop new high-order numerical methods for hyperbolic systems of nonlinear partial differential equations (PDEs) with uncertainties. The new approach is realize…