A stochastic Galerkin method with adaptive time-stepping for the Navier-Stokes equations

DOI10.1016/j.jcp.2022.111456OpenAlexW4285810876MaRDI QIDQ2168285

Bedřich Sousedík, Randy Price

Publication date: 31 August 2022

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2207.04513

zbMATH Keywords

preconditioningNavier-Stokes equationuncertainty quantificationstochastic Galerkin methodspectral stochastic finite element methods

Mathematics Subject Classification ID

Basic methods in fluid mechanics (76Mxx) Stochastic analysis (60Hxx) Probabilistic methods, stochastic differential equations (65Cxx)

Uses Software

• IFISS
• HSL_MI20

Cites Work

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• Compressive sampling of polynomial chaos expansions: convergence analysis and sampling strategies
• Time-dependent generalized polynomial chaos
• Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations
• High-order splitting methods for the incompressible Navier-Stokes equations
• Numerical integration using sparse grids
• A new stochastic approach to transient heat conduction modeling with uncertainty.
• A dynamical polynomial chaos approach for long-time evolution of SPDEs
• Modeling uncertainty in flow simulations via generalized polynomial chaos.
• Flow-driven spectral chaos (FSC) method for simulating long-time dynamics of arbitrary-order non-linear stochastic dynamical systems
• A low-rank solver for the stochastic unsteady Navier-Stokes problem
• Intrusive generalized polynomial chaos with asynchronous time integration for the solution of the unsteady Navier-Stokes equations
• Stochastic Galerkin methods for the steady-state Navier-Stokes equations
• High dimensional integration of smooth functions over cubes
• Finite Elements and Fast Iterative Solvers
• An Introduction to Computational Stochastic PDEs
• A Christoffel function weighted least squares algorithm for collocation approximations
• Adaptive Time-Stepping for Incompressible Flow Part II: Navier–Stokes Equations
• Spectral Methods for Uncertainty Quantification
• Finite Element Methods for Navier-Stokes Equations
• Mixed and Hybrid Finite Element Methods
• The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations
• A Numerical Method for the Incompressible Navier-Stokes Equations Based on an Approximate Projection
• Preconditioning Steady-State Navier--Stokes Equations with Random Data
• A Low-Rank Solver for the Navier--Stokes Equations with Uncertain Viscosity
• A HYBRID GENERALIZED POLYNOMIAL CHAOS METHOD FOR STOCHASTIC DYNAMICAL SYSTEMS
• Constructing Least-Squares Polynomial Approximations
• IFISS: A Computational Laboratory for Investigating Incompressible Flow Problems
• An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier--Stokes Equations
• Discrete least squares polynomial approximation with random evaluations − application to parametric and stochastic elliptic PDEs
• A Flexible Inner-Outer Preconditioned GMRES Algorithm
• HSL_MI20 : An efficient AMG preconditioner for finite element problems in 3D
• Adaptive Time-Stepping for Incompressible Flow Part I: Scalar Advection-Diffusion
• Dynamical Polynomial Chaos Expansions and Long Time Evolution of Differential Equations with Random Forcing
• A Newton--Galerkin Method for Fluid Flow Exhibiting Uncertain Periodic Dynamics

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