Approximation of variable density incompressible flows by means of finite elements and finite volumes - Laboratoire Interdisciplinaire des Sciences du Numérique Access content directly
Journal Articles Communications in Numerical Methods in Engineering Year : 2001

Approximation of variable density incompressible flows by means of finite elements and finite volumes

Abstract

This work describes a projection method for approximating incompressible viscous flows of nonuniform density. It is shown that unconditional stability in time is possible provided two projections are performed per time step. A finite element implementation and a finite volume one are described and compared. The performance of the two methods are tested on a Rayleigh-Taylor instability. We show that the considered problem has no inviscid smooth limit; hence confirming a conjecture by Birkho stating that the inviscid problem is not well-posed. Furthermore, we show that at even moderate Reynolds numbers, this problem is extremely sensitive to mesh refinement and to the numerical method adopted.
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Dates and versions

hal-03443376 , version 1 (01-03-2022)

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Yann Fraigneau, Jean-Luc Guermond, Luigi Quartapelle. Approximation of variable density incompressible flows by means of finite elements and finite volumes. Communications in Numerical Methods in Engineering, 2001, 17 (12), pp.893-902. ⟨10.1002/cnm.452⟩. ⟨hal-03443376⟩
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