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...
| Authors: | , |
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| Format: | article |
| Publication Date: | 2020 |
| Country: | España |
| Institution: | Universitat Politècnica de Catalunya (UPC) |
| Repository: | UPCommons. Portal del coneixement obert de la UPC |
| Language: | English |
| OAI Identifier: | oai:upcommons.upc.edu:2117/327995 |
| Online Access: | https://hdl.handle.net/2117/327995 https://dx.doi.org/10.1016/j.cma.2020.113159 |
| Access Level: | Open access |
| Keyword: | 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 |
| Summary: | 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. |
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