A fast and accurate method to solve the incompressible Navier-Stokes equations

Purpose - The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier-Stokes equations with very large time steps.Design methodology approach - The design of the paper is based on introducing the origin of th...

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Bibliographic Details
Published in:Engineering computations 2013-01, Vol.30 (2), p.197-222
Main Authors: Rodolfo Idelsohn, Sergio, Marcelo Nigro, Norberto, Marcelo Gimenez, Juan, Rossi, Riccardo, Marcelo Marti, Julio
Format: Article
Language:English
Subjects:
Accuracy
Algorithms
Anàlisi numèrica
Approximation
Atoms & subatomic particles
Benchmarking
Computer simulation
Dealing
Efficiency
Equacions de Navier-Stokes
Flow
Fluid dynamics
Fluid-structure interaction
Fluids
Incompressible fluid flows
Large time-steps
Matemàtiques i estadística
Mathematical analysis
Mathematical models
Methods
Mètodes numèrics
Navier-Stokes equations
Numerical solutions
Optimization
Particle methods
Real time CFD
Robustness
Studies
Updated Lagrangian formulations
Velocity
Àrees temàtiques de la UPC
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Summary:Purpose - The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier-Stokes equations with very large time steps.Design methodology approach - The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.Findings - The authors have found that even though this method was originally designed to deal with heterogeneous or free-surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.Originality value - With this objective in mind, the authors have chosen a number of benchmark examples and have proved that the proposed algorithm provides results which compare favourably, both in terms of solution time and accuracy achieved, with alternative approaches, implemented in in-house and commercial codes.
ISSN:0264-4401
1758-7077
DOI:10.1108/02644401311304854