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.