New high-order numerical methods for hyperbolic systems of nonlinear PDEs with uncertainties

DOI10.1007/s42967-024-00392-zMaRDI QIDQ6593789

Michael Herty, Arsen S. Iskhakov, Alexander Kurganov, Mária Lukáčová-Medvid'ová, Alina E. Chertock, Safa Janajra

Publication date: 27 August 2024

Published in: Communications on Applied Mathematics and Computation (Search for Journal in Brave)

zbMATH Keywords

finite-volume methodscentral-upwind schemeshyperbolic conservation and balance laws with uncertaintiesweighted essentially non-oscillatory (WENO) interpolations

Mathematics Subject Classification ID

Finite volume methods applied to problems in fluid mechanics (76M12) Hyperbolic conservation laws (35L65) PDEs with randomness, stochastic partial differential equations (35R60) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Cites Work

• A novel weakly-intrusive non-linear multiresolution framework for uncertainty quantification in hyperbolic partial differential equations
• A stochastic Galerkin method for the Euler equations with roe variable transformation
• Multi-level Monte Carlo finite volume methods for nonlinear systems of conservation laws in multi-dimensions
• Characterization of discontinuities in high-dimensional stochastic problems on adaptive sparse grids
• Uncertainty propagation using Wiener-Haar expansions
• Non-oscillatory central differencing for hyperbolic conservation laws
• Intrusive Galerkin methods with upwinding for uncertain nonlinear hyperbolic systems
• Uncertainty quantification for systems of conservation laws
• The stochastic finite volume method
• Monte-Carlo finite-volume methods in uncertainty quantification for hyperbolic conservation laws
• A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
• A numerical study of the performance of alternative weighted ENO methods based on various numerical fluxes for conservation law
• Roe solver with entropy corrector for uncertain hyperbolic systems
• A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations
• Scale-invariant multi-resolution alternative WENO scheme for the Euler equations
• Hyperbolicity-preserving and well-balanced stochastic Galerkin method for two-dimensional shallow water equations
• A novel and robust scale-invariant WENO scheme for hyperbolic conservation laws
• Entropy stable Galerkin methods with suitable quadrature rules for hyperbolic systems with random inputs
• Affine-invariant WENO weights and operator
• Uncertainty quantification methodology for hyperbolic systems with application to blood flow in arteries
• Hyperbolic stochastic Galerkin formulation for the \(p\)-system
• A characteristic-wise alternative WENO-Z finite difference scheme for solving the compressible multicomponent non-reactive flows in the overestimated quasi-conservative form
• A hyperbolicity-preserving discontinuous stochastic Galerkin scheme for uncertain hyperbolic systems of equations
• An improved fifth order alternative WENO-Z finite difference scheme for hyperbolic conservation laws
• A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty
• Polynomial chaos methods for hyperbolic partial differential equations. Numerical techniques for fluid dynamics problems in the presence of uncertainties
• A second-order well-balanced positivity preserving central-upwind scheme for the Saint-Venant system
• Strong Stability-Preserving High-Order Time Discretization Methods
• Semidiscrete Central-Upwind Schemes for Hyperbolic Conservation Laws and Hamilton--Jacobi Equations
• Sparse tensor multi-level Monte Carlo finite volume methods for hyperbolic conservation laws with random initial data
• Non-intrusive Uncertainty Propagation with Error Bounds for Conservation Laws Containing Discontinuities
• Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method
• Multi-level Monte Carlo Finite Volume Methods for Uncertainty Quantification in Nonlinear Systems of Balance Laws
• Multi-level Monte Carlo Finite Difference and Finite Volume Methods for Stochastic Linear Hyperbolic Systems
• Uncertainty Quantification for Hyperbolic Systems of Conservation Laws
• Multi-Element Generalized Polynomial Chaos for Arbitrary Probability Measures
• Spectral Methods for Uncertainty Quantification
• High Resolution Schemes Using Flux Limiters for Hyperbolic Conservation Laws
• On the Artificial Compression Method for Second-Order Nonoscillatory Central Difference Schemes for Systems of Conservation Laws
• Gaussian fields and random flow
• Solution of two-dimensional Riemann problems for gas dynamics without Riemann problem solvers
• Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions
• Density Estimation in Uncertainty Propagation Problems Using a Surrogate Model
• Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
• A WENO-Based Stochastic Galerkin Scheme for Ideal MHD Equations with Random Inputs
• Convergence Analysis for Stochastic Collocation Methods to Scalar Hyperbolic Equations with a Random Wave Speed
• An Alternative Formulation of Finite Difference Weighted ENO Schemes with Lax--Wendroff Time Discretization for Conservation Laws
• Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
• Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations
• A technique of treating negative weights in WENO schemes
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