14 papers
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…
Novel Adaptive Methods for Hyperbolic Conservation Laws Based on New Quasi-Linear Seventh- and Ninth-Order Schemes
Shaoshuai Chu, Pingyao Feng, Vadim A. Kolotilov +2
We develop new adaptive numerical schemes for one- and two-dimensional hyperbolic systems of conservation laws. The methodology relies on the use of a smoothness indicator to autom…
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…
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…
A Locally Divergence-Free Local Characteristic Decomposition Based Path-Conservative Central-Upwind Scheme for Ideal Magnetohydrodynamics
Shaoshuai Chu, Alexander Kurganov, Maria Lukacova-Medvidova +1
We introduce a locally divergence-free local characteristic decomposition based path-conservative central-upwind (LCD-PCCU) scheme for ideal magnetohydrodynamics (MHD) equations. T…
Novel Adaptive Schemes for Hyperbolic Conservation Laws
Shaoshuai Chu, Pingyao Feng, Vadim A. Kolotilov +2
We introduce new adaptive schemes for the one- and two-dimensional hyperbolic systems of conservation laws. Our schemes are based on an adaption strategy recently introduced in [{\…
Flux Globalization Based Well-Balanced Path-Conservative Central-Upwind Schemes for Shallow Water Linearized Moment Equations
Yangyang Cao, Qian Huang, Julian Koellermeier +2
We develop second-order path-conservative central-upwind (PCCU) schemes for the hyperbolic shallow water linearized moment equations (HSWLME), which are an extension of standard de…
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…
Central-Upwind Scheme for the Phase-Transition Traffic Flow Model
Shaoshuai Chu, Alexander Kurganov, Saeed Mohammadian +1
Phase-transition models are an important family of non-equilibrium continuum traffic flow models, offering properties like replicating complex traffic phenomena, maintaining anisot…
New More Efficient A-WENO Schemes
Shaoshuai Chu, Alexander Kurganov, Ruixiao Xin
We develop new more efficient A-WENO schemes for both hyperbolic systems of conservation laws and nonconservative hyperbolic systems. The new schemes are a very simple modification…
A Well-Balanced Fifth-Order A-WENO Scheme Based on Flux Globalization
Shaoshuai Chu, Alexander Kurganov, Ruixiao Xin
We construct a new fifth-order flux globalization based well-balanced (WB) alternative weighted essentially non-oscillatory (A-WENO) scheme for general nonconservative systems. The…
Local Characteristic Decomposition of Equilibrium Variables for Hyperbolic Systems of Balance Laws
Shaoshuai Chu, Alexander Kurganov, Mingye Na +2
This paper is concerned with high-order numerical methods for hyperbolic systems of balance laws. Such methods are typically based on high-order piecewise polynomial reconstruction…
CWENO Interpolation for Non-Oscillatory Stochastic Collocation in Uncertainty Quantification Problems
Alina Chertock, Arsen S. Iskhakov, Anna Iskhakova +1
Uncertainty quantification (UQ) in mathematical models is essential for accurately predicting system behavior under variability. This study provides guidance on method selection fo…
Birth, interactions, and evolution over topography of solitons in Serre-Green-Naghdi model
Qingcheng Fu, Alexander Kurganov, Mingye Na +1
New evidence of surprising robustness of solitary-wave solutions of the Serre-Green-Naghdi (SGN) equations is presented on the basis of high-resolution numerical simulations conduc…