Open Access

ARTICLE

An Immersed Method Based on Cut-Cells for the Simulation of 2D Incompressible Fluid Flows Past Solid Structures

François Bouchon^{1, *}, Thierry Dubois¹, Nicolas James²

1 Université Clermont Auvergne, CNRS, LMBP, F-63000 CLERMONT-FERRAND, France.
2 Laboratoire de Mathématiques et Applications UMR 7348, Université de Poitiers, Téléport 2-B.P. 30179, Boulevard Marie et Pierre Curie, 86962 Futuroscope Chasseneuil Cedex, France.
* Corresponding Author: François Bouchon. Email: francois.bouchon@uca.fr.

(This article belongs to the Special Issue: Recent Developments of Immersed Methods for Fluid-structure Interactions)

Computer Modeling in Engineering & Sciences 2019, 119(1), 165-184. https://doi.org/10.32604/cmes.2019.04841

Abstract

We present a cut-cell method for the simulation of 2D incompressible flows past obstacles. It consists in using the MAC scheme on cartesian grids and imposing Dirchlet boundary conditions for the velocity field on the boundary of solid structures following the Shortley-Weller formulation. In order to ensure local conservation properties, viscous and convecting terms are discretized in a finite volume way. The scheme is second order implicit in time for the linear part, the linear systems are solved by the use of the capacitance matrix method for non-moving obstacles. Numerical results of flows around an impulsively started circular cylinder are presented which confirm the efficiency of the method, for Reynolds numbers 1000 and 3000. An example of flows around a moving rigid body at Reynolds number 800 is also shown, a solver using the PETSc-Library has been prefered in this context to solve the linear systems.

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