A Posteriori Error Estimators and Adaptive Mesh-Refinement for a Mixed Finite Element Discretization of the Navier-Stokes Equations

1990 ◽  
pp. 145-152 ◽  
Author(s):  
R. Verfürth
Keyword(s):  
Adaptive Mesh Refinement ◽  
Stokes Equations ◽  
Mixed Finite Element ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Element Discretization ◽  
Error Estimators ◽  
Posteriori Error Estimators

scholarly journals D2.3. Adjoint-based error estimation routines

2021 ◽  
Author(s):  
B. Keith ◽  
A. Apostolatos ◽  
A. Kodakkal ◽  
R. Rossi ◽  
R. Tosi ◽  
...  
Keyword(s):  
Error Estimation ◽  
Stokes Equations ◽  
Model Problem ◽  
State Of The Art ◽  
Adaptive Mesh ◽  
Posteriori Error ◽  
Navier Stokes ◽  
Error Estimator ◽  
Navier Stokes Equations ◽  
A Posteriori Error

This document presents a simple and ecient strategy for adaptive mesh renement (AMR) and a posteriori error estimation for the transient incompressible Navier{Stokes equations. This strategy is informed by the work of Prudhomme and Oden [22, 23] as well as modern goal-oriented methods such as [5]. The methods described in this document have been implemented in the Kratos Multiphysics software and uploaded to https://zenodo.org [27].1 This document includes: A review of the state-of-the-art in solution-oriented and goal-oriented AMR. The description of a 2D benchmark model problem of immediate relevance to the objectives of the ExaQUte project. The denition and a brief mathematical summary of the error estimator(s). The results obtained. A description of the API.

scholarly journals A Material Interface Transition Algorithm for Multiphase Flow

2008 ◽  
Author(s):  
Marianne M. Francois ◽  
Robert B. Lowrie ◽  
Edward D. Dendy
Keyword(s):  
Adaptive Mesh Refinement ◽  
Stokes Equations ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Navier Stokes ◽  
Material Interface ◽  
Navier Stokes Equations ◽  
Interface Reconstruction ◽  
Rayleigh Taylor Instability ◽  
Interface Treatment

Volume tracking method, also referred to as the volume-of-fluid (VOF) method introduces “numerical surface tension” that breaks a filament into a series of droplets whenever the filament is under-resolved. Adaptive mesh refinement can help avoid under-resolution, but a fully-developed flow will still generate filaments that cannot be resolved without enormous computational cost. We propose a complementary new approach that consists of transitioning to a continuous interface representation (i.e. without interface reconstruction) in regions of under-resolved interfacial curvature where volume tracking has become erroneous. The price of the continuous interface treatment is a small amount of numerical mass diffusion, even if the physical interface is immiscible. However, we have found that for certain measures, the overall accuracy is greatly improved by using our transitioning algorithm. The algorithm is developed in the context of the single fluid formulation of the incompressible Navier-Stokes equations. Numerical standard vortices advection test cases and Rayleigh-Taylor instability computations are presented to illustrate the transition algorithm potential.

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