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

Sergio Rodolfo Idelsohn (Intitució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain and Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Polytechnic University of Catalonia (UPC), Barcelona, Spain)
Norberto Marcelo Nigro (Centro Internacional de Métodos Computacionales en Ingeniería, CIMEC‐INTEC‐CONICET‐UN, Santa Fe, Argentina)
Juan Marcelo Gimenez (Centro Internacional de Métodos Computacionales en Ingeniería, CIMEC‐INTEC‐CONICET‐UN, Santa Fe, Argentina)
Riccardo Rossi (Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Polytechnic University of Catalonia (UPC), Barcelona, Spain)
Julio Marcelo Marti (Centro Internacional de Métodos Numéricos en Ingeniería (CIMNE), Polytechnic University of Catalonia (UPC), Barcelona, Spain)

Engineering Computations

ISSN: 0264-4401

Publication date: 22 February 2013

Abstract

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.

Keywords

Citation

Rodolfo Idelsohn, S., Marcelo Nigro, N., Marcelo Gimenez, J., Rossi, R. and Marcelo Marti, J. (2013), "A fast and accurate method to solve the incompressible Navier‐Stokes equations", Engineering Computations, Vol. 30 No. 2, pp. 197-222. https://doi.org/10.1108/02644401311304854

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Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited

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