Analysis, extensions and applications of the Finite-Volume...

ADVANCED STUDIES AND RESEARCH CENTER Str. Verii, Nr.4, sector 2 – 020723, Bucuresti

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J40/9389/2001 CUI RO 14283349

IBAN: RO21 RZBR 0000 0600 0286 2000, deschis la Raiffeisen Bank, Agentia Amzei (LEI)

IBAN: RO85 RZBR 0000 0600 0894 7792, deschis la Raiffeisen Bank, Agentia Amzei (EURO)

IBAN: RO06 TREZ 7035 069X XX00 5885, deschis la Trezoreria Sectorului 3, Bucuresti

Analysis, extensions and applications of the Finite-Volume Particle Method (FVPM)

PN-II-RU-TE-2011-3-0256

- Synthesis of the technical report -

Phase 3: Intermediary phase

Authors: Delia Teleagă, Eliza Munteanu Project Coordinator: Delia Teleagă

December 2012

mailto:[email protected]



J40/9389/2001 CUI RO 14283349




Synthesis of the Technical report for June - December 2012

The activities of the phase 3 (June-December 2012) aimed to develop FVPM algorithms for inviscid and viscous

incompressible flows, implementation and testing of the respective algorithms.

It was developed a FVPM scheme for solving Euler equations, as well as the addition of a viscous flow in order to solve the

Navier Stokes equations. The schemes were tested on several classic problems on validation of the codes for the

computational fluid dynamics for incompressible flows:

- the problem of a flow in a squared, closed cavity;

- the unsteady flow around a circular cylinder.

1. Aplication for incompressible flows

2.1. The problem of a flow in a squared, closed cavity

The problem of a flow in a squared, closed cavity, in which the upper wall is moving with a constant velocity U and the

fluid is in repaos (Fig. 3) is a well-known problem and oft studied problem to test numerical methods for solving

incompressible Navier-Stokes equations (e.g. [1, 2]).

Figure 1 Problem geometry

Figure 2 Flow lines of the stationary solution, for Reynolds = 400. For this simulation, the FVPM scheme with 40.000 particles,

corresponding to a mesh with 200 x 200 nodes.




J40/9389/2001 CUI RO 14283349




Figure 3 Contour lines of velocity (u –left, v – right) for the cavity problem

Figure 4 Velocity graphics for a cut throyh the middle of the domain (left –u for x = L/2, right –v for y = L/2)

The results presented in Fig. 4, 5 and 6 are similar to the results obtained in literature by other authors when using first order

schemes (e.g. [1, 2]).

2.2. Non-stationary flow around a circular cylinder [3, 4]

For this simulation the FVPM scheme with 150 x 450 particles distributed in a rectangular domain (Figure 7) was applied,

with inflow boundary conditions at the left boundary, with wall b.c. at the upper and bottom boundary and with outflow b.c.

at the right boundary. In Fig. 7 si 8 are presented results obtained for Reynolds = 1000.




J40/9389/2001 CUI RO 14283349




Figure 5 Contour lines of the velocity (u – upper, v – botom) for Re = 1000

Figure 6 Flow lines for Re = 1000,at different time moments. The building of von Karman vortices may be observed.




J40/9389/2001 CUI RO 14283349




3. Bibliografie

[1] Ghia, Ghia, and Shin (1982), High-Re solutions for incompressible flow using the Navier-Stokes equations and a

multigrid method, Journal of Computational Physics, Vol. 48, pp. 387-411

[2] Erturk, Corke, and Gokcol (2005), Numerical Solutions of 2-D Steady Incompressible Driven Cavity Flow at High

Reynolds Numbers, International Journal for Numerical Methods in Fluids, Vol. 48, pp. 747-774

[3] Hirsch C. (1990), Numerical Computation of Internal and External Flow, John Wiley and Sons, New York

[4] Anderson, J.D., (2001), Fundamentals of Aerodynamics, 3rd Ed., McGraw-Hill, New York

Project coordinator,

Dr. Delia TELEAGA


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