Regularized Reduced Order Models for a Stochastic Burgers Equation
arXiv:1701.01155
Abstract
In this paper, we study the numerical stability of reduced order models for convection-dominated stochastic systems in a relatively simple setting: a stochastic Burgers equation with linear multiplicative noise. Our preliminary results suggest that, in a convection-dominated regime, standard reduced order models yield inaccurate results in the form of spurious numerical oscillations. To alleviate these oscillations, we use the Leray reduced order model, which increases the numerical stability of the standard model by smoothing (regularizing) the convective term with an explicit spatial filter. The Leray reduced order model yields significantly better results than the standard reduced order model and is more robust with respect to changes in the strength of the noise.
References in corpus (7)
- The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
- Proper Orthogonal Decomposition Closure Models For Turbulent Flows: A Numerical Comparison
- A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number
- Regularization modeling for large-eddy simulation
- Galerkin approximations for the stochastic Burgers equation
- Multiplicative Noise in Non-equilibrium Phase Transitions: A tutorial
- Non-Markovian Reduced Systems for Stochastic Partial Differential Equations: The Additive Noise Case
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- Consistency of the Full and Reduced Order Models for Evolve-Filter-Relax Regularization of Convection-Dominated, Marginally-Resolved Flows
- Parameter Estimation and Adaptive Solution of the Leray-Burgers Equation Using Physics-Informed Neural Networks
- Nonintrusive Stabilization of Reduced Order Models for Uncertainty Quantification of Time-Dependent Convection-Dominated Flows