### Numerical Simulation Of Free Surface Flows With Volume Control

#### Abstract

In previous works (Battaglia et al, Mecánica Computacional, vol. XXIV, pp. 105-116,

Buenos Aires, Argentina, Nov. 2005), the free surface movement of a fluid flow of an incompressible

and viscous fluid was followed by a mesh-movement technique, where the update of the free surface

location was smoothed in order to prevent numerical instability due to a fully explicit discretization of

the differential equation that describes the free surface kinematics. Unlike fluid flows in closed domains,

in cases where the movement of the free surface coexists with inflow and outflow sections with fixed

parameters, the volume of the fluid could grow or decrease in an unexpected way, i.e., the initial parameters

for incoming velocity and discharge pressure could not be appropriate for keeping bounded

the volume of the fluid, leading to somewhat artificial free surface displacements. Then, a control technique

is shown for modifying some parameters in order to balance the flow between successive steps

during the time marching simulation, interacting with the multi-physics finite element code PETSc-FEM

(http://www.cimec.org.ar/petscfem/). This control is achieved with an extension of the hooks technology

presented in Battaglia et al. (Mecánica Computacional, vol. XXIII, pp. 3119-3132, Bariloche,

Argentina, Nov. 2004). As a numerical example, the development of the free surface of an axisymmetric

vertical vortex is simulated with this volume control strategy and a finite element (FE) computation.

Buenos Aires, Argentina, Nov. 2005), the free surface movement of a fluid flow of an incompressible

and viscous fluid was followed by a mesh-movement technique, where the update of the free surface

location was smoothed in order to prevent numerical instability due to a fully explicit discretization of

the differential equation that describes the free surface kinematics. Unlike fluid flows in closed domains,

in cases where the movement of the free surface coexists with inflow and outflow sections with fixed

parameters, the volume of the fluid could grow or decrease in an unexpected way, i.e., the initial parameters

for incoming velocity and discharge pressure could not be appropriate for keeping bounded

the volume of the fluid, leading to somewhat artificial free surface displacements. Then, a control technique

is shown for modifying some parameters in order to balance the flow between successive steps

during the time marching simulation, interacting with the multi-physics finite element code PETSc-FEM

(http://www.cimec.org.ar/petscfem/). This control is achieved with an extension of the hooks technology

presented in Battaglia et al. (Mecánica Computacional, vol. XXIII, pp. 3119-3132, Bariloche,

Argentina, Nov. 2004). As a numerical example, the development of the free surface of an axisymmetric

vertical vortex is simulated with this volume control strategy and a finite element (FE) computation.

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Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**Asociación Argentina de Mecánica Computacional**Güemes 3450

S3000GLN Santa Fe, Argentina

Phone: 54-342-4511594 / 4511595 Int. 1006

Fax: 54-342-4511169

E-mail: amca(at)santafe-conicet.gov.ar

**ISSN 2591-3522**