Element boundary terms in reduced order models for flow problems: domain decomposition and adaptive coarse mesh hyper-reduction

In this paper we present a finite-element based reduced order model and, in particular, we consider two aspects related to the introduction of inter-element boundary terms in the formulation. The first is a domain decomposition strategy in which the transmission conditions involve boundary terms to...

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Detalles Bibliográficos
Autores: Reyes, Ricardo|||0000-0003-0140-9564, Codina, Ramon|||0000-0002-7412-778X
Tipo de recurso: artículo
Fecha de publicación:2020
País:España
Institución:Universitat Politècnica de Catalunya (UPC)
Repositorio:UPCommons. Portal del coneixement obert de la UPC
Idioma:inglés
OAI Identifier:oai:upcommons.upc.edu:2117/327995
Acceso en línea:https://hdl.handle.net/2117/327995
https://dx.doi.org/10.1016/j.cma.2020.113159
Access Level:acceso abierto
Palabra clave:Decomposition (Mathematics)
Fluid mechanics--Mathematical models
Reduced order model (ROM)
Variational multi-scale (VMS) method
Boundary subscales
Hyper-reduction
Adaptive mesh refinement (AMR)
a posteriori error estimates
Descomposició (Matemàtica)
Mecànica de fluids -- Mètodes numèrics
Àrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes numèrics
Àrees temàtiques de la UPC::Física::Física de fluids::Flux de fluids
Descripción
Sumario:In this paper we present a finite-element based reduced order model and, in particular, we consider two aspects related to the introduction of inter-element boundary terms in the formulation. The first is a domain decomposition strategy in which the transmission conditions involve boundary terms to account for non-matching meshes and discontinuous physical properties. The second is a coarse mesh hyper-reduction for which we propose an adaptive refinement driven by an a posteriori error estimator that contains element boundary terms. As the finite element full order model, the reduced order model is based on the Variational Multi-Scale framework, with sub-grid scales defined not only in the element interiors, but also on the inter-element boundaries. We present some examples of application using the incompressible Navier–Stokes equations and the Boussinesq approximation.