Stabilised Finite Element for High Reynolds Number, LES and Free Surface flow Problems

We propose a stabilized finite element method to address complex high Reynolds flows with free surface. An implicit stabilized finite element method (SFEM) is used for solving the incompressible two-phase Navier-Stokes equations in three-dimensions. A novel approach to deal with turbulent two-phase flows is highlighted by coupling a local convected levelset method to a Large Eddy simulation turbulent modeling. A comparison between the static and dynamic eddy-viscosity models is analyzed. We assess the behaviour and accuracy of the proposed stabilized finite element method coupled to the two-phase turbulent approximation in the simulation of complex 3D flows, such as the flow in a partially filled two communicating tanks. Results are compared with the experimental data and show that the present implementation is able to exhibit good stability and accuracy properties for high Reynolds number flows using unstructured meshes.

[1]  T. Hughes,et al.  The variational multiscale method—a paradigm for computational mechanics , 1998 .

[2]  Pierre Sagaut,et al.  Towards large eddy simulation of isothermal two-phase flows: Governing equations and a priori tests , 2007 .

[3]  Jean-Francois Hetu,et al.  Finite element solution of three-dimensional turbulent flows applied to mold-filling problems , 2000 .

[4]  Pierre Sagaut,et al.  Numerical simulation of phase separation and a priori two-phase LES filtering , 2008 .

[5]  T. Coupez,et al.  Convected level set method for the numerical simulation of fluid buckling , 2011 .

[6]  R. Codina.  Stabilized finite element approximation of transient incompressible flows using orthogonal subscales , 2002 .

[7]  Pierre Lubin,et al.  Three-dimensional Large Eddy Simulation of , 2006 .

[8]  R. Courant,et al.  Über die partiellen Differenzengleichungen der mathematischen Physik , 1928 .

[9]  Tayfun E. Tezduyar,et al.  Collapse of a Liquid Column: Numerical Simulation and Experimental Validation , 2007 .

[10]  Phung Dang Hieu,et al.  Numerical simulation of breaking waves using a two-phase flow model , 2004 .

[11]  Mohammad Javad Ketabdari,et al.  Simulation of waves group propagation and breaking in coastal zone using a Navier–Stokes solver with an improved VOF free surface treatment , 2008 .

[12]  Hamn-Ching Chen,et al.  CFD simulations of wave–current-body interactions including greenwater and wet deck slamming , 2009 .

[13]  D. Lilly,et al.  A proposed modification of the Germano subgrid‐scale closure method , 1992 .

[14]  P. Moin,et al.  A dynamic subgrid‐scale eddy viscosity model , 1990 .

[15]  Julien De Rouck,et al.  Interactions of breaking waves with a current over cut cells , 2007, J. Comput. Phys..

[16]  Tayfun E. Tezduyar,et al.  Finite element stabilization parameters computed from element matrices and vectors , 2000 .

[17]  Elie Hachem,et al.  Stabilized finite element method for heat transfer and turbulent flows inside industrial furnaces , 2009 .

[18]  J. Smagorinsky,et al.  GENERAL CIRCULATION EXPERIMENTS WITH THE PRIMITIVE EQUATIONS , 1963 .

[19]  B. Launder,et al.  Lectures in mathematical models of turbulence , 1972 .