An Evolve-Filter-Relax Stabilized Reduced Order Stochastic Collocation Method for the Time-Dependent Navier--Stokes Equations
<|begin_of_text|><|start_header_id|>system<|end_header_id|> You are a research archivist expert in dataset metadata. Answer the question truthfully.  <|eot_id|><|start_header_id|>user<|end_header_id|> Here is the Description of a dataset. Description:'In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier--Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean Re = 100' . Please return only a json list of at most 3 Keywords corresponding to the Description:.<|eot_id|><|start_header_id|>assistant<|end_header_id|> {"Answer" : ["convection-dominated regimes","evolve-filter-relax algorithm","evolve-filter-relax stabilized reduced order stochastic collocation method","filter-based stabilization","novel high-order ROM differential filter","numerical oscillations","numerical simulation","random viscosity","reduced order models","reynolds number","standard ROMs","stochastic collocation methods","time-dependent Navier-Stokes equations","two-dimensional flow past circular cylinder","uncertainty quantification"]} <|eot_id|>
 Here is the Description of a dataset. Description:'In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier--Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean Re = 100' . Please return only a json list of at most 3 Keywords corresponding to the Description:.
In this paper, we propose a filter-based stabilization of reduced order models (ROMs) for uncertainty quantification (UQ) of the time-dependent Navier--Stokes equations in convection-dominated regimes. We propose a novel high-order ROM differential filter and use it in conjunction with an evolve-filter-relax (EFR) algorithm to attenuate the numerical oscillations of standard ROMs. We also examine how stochastic collocation methods can be combined with the EFR algorithm for efficient UQ of fluid flows. We test the new framework in the numerical simulation of a two-dimensional flow past a circular cylinder with a random viscosity that yields a random Reynolds number with mean Re = 100
convection-dominated regimes; evolve-filter-relax algorithm; evolve-filter-relax stabilized reduced order stochastic collocation method; filter-based stabilization; novel high-order ROM differential filter; numerical oscillations; numerical simulation; random viscosity; reduced order models; reynolds number; standard ROMs; stochastic collocation methods; time-dependent Navier-Stokes equations; two-dimensional flow past circular cylinder; uncertainty quantification