A high-order local projection stabilization method for natural convection problems
type: Item
instance of: scholarly article
title: A high-order local projection stabilization method for natural convection problems
zbMATH Open document ID: 1397.65181
author: Samuele Rubino
author: Isabel Sánchez Muñoz
author: Tomás Chacón Rebollo
author: Macarena Gómez Mármol
author: Frédéric Hecht
published in: Journal of Scientific Computing
publication date: 2018-04-12T00:00:00Z
review text: The paper is concerned with the analysis of the local projection stabilization finite element method for natural convection problems governed by the Boussinesq-Navier-Stokes systems. Since the standard finite element method for these systems typically leads to solutions with spurious oscillations at high Rayleigh numbers, the authors focus on the stabilization of the method. They propose a local projection stabilization that is based on the interpolation-stabilized structure rather than on the standard projection-stabilized structure. The authors prove that the proposed scheme is stable and convergent, and they derive optimal error estimates. To illustrate the efficiency and reliability of the method, the numerical experiments are provided for the 2D motion of a fluid in a square cavity with differentially heated side walls at high Rayleigh numbers and the results are compared with benchmark solutions. The method gives sufficiently accurate solutions on relatively coarse grids.
reviewed by: Dana Černá
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76R10
Mathematics Subject Classification ID: 65M15
Mathematics Subject Classification ID: 76M10
zbMATH DE Number: 6858868
zbMATH Keywords: Boussinesq approximation
zbMATH Keywords: thermally coupled flows
zbMATH Keywords: natural convection
zbMATH Keywords: local projection stabilization method
zbMATH Keywords: finite element method
zbMATH Keywords: high Rayleigh number
describes a project that uses: FreeFem++
MaRDI profile type: Publication
full work available at URL: s10915-017-0469-9
OpenAlex ID: W2624315217
cites work: Analysis of a Full Space–Time Discretization of the Navier–Stokes Equations by a Local Projection Stabilization Method
cites work: A review of variational multiscale methods for the simulation of turbulent incompressible flows
cites work: Discontinuous Galerkin time stepping with local projection stabilization for transient convection-diffusion-reaction problems
cites work: Local projection FEM stabilization for the time‐dependent incompressible <scp>N</scp>avier–<scp>S</scp>tokes problem
cites work: Consistent Local Projection Stabilized Finite Element Methods
cites work: A local projection stabilization finite element method with nonlinear crosswind diffusion for convection-diffusion-reaction equations
cites work: Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows
cites work: A finite element pressure gradient stabilization for the Stokes equations based on local projections
cites work: Q4823208
cites work: A second order characteristics finite element scheme for natural convection problems
cites work: Density results in Sobolev spaces whose elements vanish on a part of the boundary
cites work: Variational discretization of elliptic boundary value problems.
cites work: An analysis of the finite element method for natural convection problems
cites work: Error analysis for finite element methods for steady natural convection problems
cites work: Local Projection Stabilization for the Oseen Problem and its Interpretation as a Variational Multiscale Method
cites work: Stabilized finite element methods for the generalized Oseen problem
cites work: Continuous interior penalty finite element method for the time-dependent Navier-Stokes equations: space discretization and convergence
cites work: A term by term stabilization algorithm for finite element solution of incompressible flow problems
cites work: A high order term-by-term stabilization solver for incompressible flow problems
cites work: A reduced discrete inf-sup condition inLpfor incompressible flows and application
cites work: Numerical analysis of penalty stabilized finite element discretizations of evolution Navier-Stokes equations
cites work: Finite Element Approximation of an Unsteady Projection-Based VMS Turbulence Model with Wall Laws
cites work: Numerical analysis of a finite element projection-based VMS turbulence model with wall laws
cites work: Numerical approximation of the Smagorinsky turbulence model applied to the primitive equations of the ocean
cites work: Mathematical and numerical foundations of turbulence models and applications
cites work: A projection-based stabilized finite element method for steady-state natural convection problem
cites work: Dynamic subscales in the finite element approximation of thermally coupled incompressible flows
cites work: Finite element approximation of turbulent thermally coupled incompressible flows with numerical sub‐grid scale modelling
cites work: Time dependent subscales in the stabilized finite element approximation of incompressible flow problems
cites work: Local projection stabilization for the Oseen problem
cites work: A steepest gradient method for optimum structural design
cites work: Q2702181
cites work: Q3865727
cites work: The two-level local projection stabilization as an enriched one-level approach
cites work: New development in freefem++
cites work: Korn’s Inequalities and Their Applications in Continuum Mechanics
cites work: The variational multiscale method -- a paradigm for computational mechanics
cites work: A Generalization of the Local Projection Stabilization for Convection-Diffusion-Reaction Equations
cites work: Local projection stabilization for advection-diffusion-reaction problems: one-level vs. two-level approach
cites work: A PROJECTION-BASED VARIATIONAL MULTISCALE METHOD FOR LARGE-EDDY SIMULATION WITH APPLICATION TO NON-ISOTHERMAL FREE CONVECTION PROBLEMS
cites work: An explicit finite element algorithm for convection heat transfer problems
cites work: Characteristic‐based‐split (CBS) algorithm for incompressible flow problems with heat transfer
cites work: A unified convergence analysis for local projection stabilisations applied to the Oseen problem
cites work: Stabilization of local projection type applied to convection-diffusion problems with mixed boundary conditions
cites work: Local projection type stabilization applied to inf-sup stable discretizations of the Oseen problem
cites work: Existence and nonuniqueness of rectangular solutions of the Benard problem
cites work: Robust Numerical Methods for Singularly Perturbed Differential Equations
cites work: Compact sets in the space \(L^ p(0,T;B)\)
cites work: Q3585683
cites work: Error analysis of a fully discrete finite element variational multiscale method for the natural convection problem
DOI: 10.1007/S10915-017-0469-9

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