A Lagrangian fractional step method for the incompressible Navier-Stokes equations on a periodic domain
type: Item
instance of: scholarly article
title: A Lagrangian fractional step method for the incompressible Navier-Stokes equations on a periodic domain
zbMATH Open document ID: 0658.76026
DOI: 10.1016/0021-9991(87)90189-6
author: C. Börgers
author: Charles S. Peskin
published in: Journal of Computational Physics
publication date: 1987-01-01T00:00:00Z
full work available at URL: 2mm3x4sq
review text: A new Lagrangian method is presented for solving the two-dimensional incompressible Navier-Stokes equations in primitive variables on a periodic domain. A collection of N moving points (fluid markers) serve as a grid. The associated Voronoi diagram is used for the construction of the finite-difference operators corresponding to the divergence, gradient and Laplacian. A Lagrangian version of Chorin's projection method is considered for the time discretization. This requires the solution of a Poisson equation for the pressure and a Helmholtz equation for each velocity component at each time step. A two-grid method is proposed for solving the discretized equations. The second grid involved is not obtained by coarsening but by regularization: A regular grid of roughly N points is introduced. On this grid the equations are solved exactly by using Fast Fourier Transform. Numerical results are reported for four test problems.
Mathematics Subject Classification ID: 76D05
Mathematics Subject Classification ID: 65M99
Mathematics Subject Classification ID: 65N99
zbMATH DE Number: 4076814
zbMATH Keywords: Lagrangian method
zbMATH Keywords: two-dimensional incompressible Navier-Stokes equations
zbMATH Keywords: periodic domain
zbMATH Keywords: Voronoi diagram
zbMATH Keywords: finite-difference operators
zbMATH Keywords: Chorin's projection method
zbMATH Keywords: time discretization
zbMATH Keywords: Fast Fourier Transform
reviewed by: Walter Zulehner
MaRDI profile type: Publication
OpenAlex ID: W2016740037
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description: scientific article; zbMATH DE number 4076814