An Edge-based Interface Tracking (EBIT) Method for Multiphase-flows Simulation with Surface Tension

We present a novel Front-Tracking method, the Edge-Based Interface Tracking (EBIT) method for multiphase flow simulations. In the EBIT method, the markers are located on the grid edges and the interface can be reconstructed without storing the connectivity of the markers. This feature makes the process of marker addition or removal easier than in the traditional Front-Tracking method. The EBIT method also allows almost automatic parallelization due to the lack of explicit connectivity. In a previous journal article we have presented the kinematic part of the EBIT method, that includes the algorithms for interface linear reconstruction and advection. Here, we complete the presentation of the EBIT method and combine the kinematic algorithm with a Navier--Stokes solver. To identify the reference phase and to distinguish ambiguous topological configurations, we introduce a new feature: the Color Vertex. For the coupling with the Navier--Stokes equations, we first calculate volume fractions from the position of the markers and the Color Vertex, then viscosity and density fields from the computed volume fractions and finally surface tension stresses with the Height-Function method. In addition, an automatic topology change algorithm is implemented into the EBIT method, making it possible the simulation of more complex flows. A two-dimensional version of the EBIT method has been implemented in the open-source Basilisk platform, and validated with five standard test cases: (1) translation with uniform velocity, (2) single vortex, (3) capillary wave, (4) Rayleigh-Taylor instability and (5) rising bubble. The results are compared with those obtained with the Volume-of-Fluid (VOF) method already implemented in Basilisk

A new projection method for Navier-stokes equations by using Raviart-thomas finite element

Computational Fluid Dynamics codes usually adopt velocity-pressure splitting to reduce the computational effort in the solution of the Navier-Stokes equations. In standard projection methods, the finite element approximations show difficulties to find a solution with discrete free-divergence velocity field in all space points. In this work, a new velocity-pressure method for Navier-Stokes equations that projects the velocity field inside the discrete free-divergence velocity space is presented. This algorithm computes the velocity field on the discrete free-divergence space by using Raviart-Thomas finite elements. The projection is obtained by the minimization of the distance, over the discrete free-divergence space, between the auxiliary field and the desired Raviart-Thomas interpolation space. The Raviart-Thomas discretization is based on the quadrilateral and hexahedral finite element space and therefore the divergence mimetic computational approach is used to avoid the well-known degradation of the divergence term convergence. The auxiliary velocity field is obtained by solving the velocity-pressure split system used in the classical Chorin­Temam algorithm. The pressure is recovered by the orthogonal space to the projection on the Raviart-Thomas interpolation space. The method is investigated with an explicit and semi-implicit treatment of the pressure terms. The issues on boundary conditions and the errors in the reproducibility of the tangential components are investigated. Several numerical examples are reported to support this new projection method

Parallel simulation of multiphase flows using octree adaptivity and the volume-of-fluid method

International audienceWe describe computations performed using the Gerris code, an open-source software implementing finite volumesolvers on an octree adaptive grid together with a piecewise linear volume of fluid interface tracking method. Theparallelisation of Gerris is achieved by domain decomposition. We show examples of the capabilities of Gerris onseveral types of problems. The impact of a droplet on a layer of the same liquid results in the formation of a thinair layer trapped between the droplet and the liquid layer that the adaptive refinement allows to capture. It isfollowed by the jetting of a thin corolla emerging from below the impacting droplet. The jet atomization problemis another extremely challenging computational problem, in which a large number of small scales are generated.Finally we show an example of a turbulent jet computation in an equivalent resolution of 6 × 10243 cells. Thejet simulation is based on the configuration of the Deepwater Horizon oil lea

FEMuS-Platform: a numerical platform for multiscale and multiphysics code coupling

Nowadays, many open-source numerical codes are available to solve physical problems in structural mechanics, fluid flow, heat transfer, and neutron diffusion. However, even if these codes are often highly specialized in the numerical simulation of a particular type of physics, none of them allows simulating complex systems involving all the physical problems mentioned above. In this work we present a numerical framework, based on the SALOME platform, developed to perform multiscale and multiphysics simulations involving all the mentioned physical problems. In particular, the developed numerical platform includes the multigrid finite element in-house code FEMuS for heat transfer, fluid flow, turbulence and fluid-structure modeling; the open-source finite volume CFD software OpenFOAM; the multiscale neutronic code DONJON-DRAGON; and a system-scale code used for thermal-hydraulic simulations. Efficient data exchange among these codes is performed within computer memory by using the MED libraries, provided by the SALOME platform