Hyperbolicity-Preserving and Well-Balanced Stochastic Galerkin Method for Shallow Water Equations

DOI10.1137/20M1360736zbMath1471.65114arXiv2008.08154OpenAlexW3133897768MaRDI QIDQ5857733

Yekaterina Epshteyn, Dihan Dai, Akil C. Narayan

Publication date: 7 April 2021

Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2008.08154

zbMATH Keywords

finite volume methodshallow water equationsstochastic Galerkin methodhyperbolic systems of conservation law and balance laws

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) PDEs with randomness, stochastic partial differential equations (35R60) Finite volume methods for initial value and initial-boundary value problems involving PDEs (65M08)

Related Items (7)

Multi-Modes Multiscale Approach of Heat Transfer Problems in Heterogeneous Solids with Uncertain Thermal Conductivity ⋮ Hyperbolicity-preserving and well-balanced stochastic Galerkin method for two-dimensional shallow water equations ⋮ Entropy stable Galerkin methods with suitable quadrature rules for hyperbolic systems with random inputs ⋮ Cross-mode stabilized stochastic shallow water systems using stochastic finite element methods ⋮ Turnpike properties of optimal boundary control problems with random linear hyperbolic systems ⋮ A flux reconstruction stochastic Galerkin scheme for hyperbolic conservation laws ⋮ A realizable filtered intrusive polynomial moment method

Uses Software

• ALEA

Cites Work

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• A stochastic Galerkin method for the Euler equations with roe variable transformation
• Adaptive stochastic Galerkin FEM
• 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
• Efficient stochastic Galerkin methods for random diffusion equations
• A stochastic Galerkin method for first-order quasilinear hyperbolic systems with uncertainty
• A kinetic scheme for the Saint-Venant system with a source term
• New high-resolution central schemes for nonlinear conservation laws and convection-diffusion equations
• A hyperbolicity-preserving stochastic Galerkin approximation for uncertain hyperbolic systems of equations
• A gPC-intrusive Monte-Carlo scheme for the resolution of the uncertain linear Boltzmann equation
• Hyperbolic stochastic Galerkin formulation for the \(p\)-system
• Filtered stochastic Galerkin methods for hyperbolic equations
• Well-balanced positivity preserving central-upwind scheme with a novel wet/dry reconstruction on triangular grids for the Saint-Venant system
• A study of hyperbolicity of kinetic stochastic Galerkin system for the isentropic Euler equations with uncertainty
• A stochastic Galerkin method for the Boltzmann equation with uncertainty
• 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
• Well-balanced positivity preserving central-upwind scheme on triangular grids for the Saint-Venant system
• On the convergence of generalized polynomial chaos expansions
• Robust Uncertainty Propagation in Systems of Conservation Laws with the Entropy Closure Method
• A Stochastic Galerkin Method for the Boltzmann Equation with Multi-Dimensional Random Inputs Using Sparse Wavelet Bases
• Adaptive Semidiscrete Central-Upwind Schemes for Nonconvex Hyperbolic Conservation Laws
• Spectral Methods for Uncertainty Quantification
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• Central-Upwind Schemes for the Saint-Venant System
• A Fast and Stable Well-Balanced Scheme with Hydrostatic Reconstruction for Shallow Water Flows
• Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes
• Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• Multilevel Monte Carlo Finite Volume Methods for Shallow Water Equations with Uncertain Topography in Multi-dimensions
• Entropies and Symmetrization of Hyperbolic Stochastic Galerkin Formulations
• Finite-volume schemes for shallow-water equations
• High-Order Collocation Methods for Differential Equations with Random Inputs
• The proof of Tchakaloff’s Theorem
• The Homogeneous Chaos

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