Projection method for droplet dynamics on groove-textured surface with merging and splitting

The geometric motion of small droplets placed on an impermeable textured substrate is mainly driven by the capillary effect, the competition among surface tensions of three phases at the moving contact lines, and the impermeable substrate obstacle. After introducing an infinite dimensional manifold with an admissible tangent space on the boundary of the manifold, by Onsager's principle for an obstacle problem, we derive the associated parabolic variational inequalities. These variational inequalities can be used to simulate the contact line dynamics with unavoidable merging and splitting of droplets due to the impermeable obstacle. To efficiently solve the parabolic variational inequality, we propose an unconditional stable explicit boundary updating scheme coupled with a projection method. The explicit boundary updating efficiently decouples the computation of the motion by mean curvature of the capillary surface and the moving contact lines. Meanwhile, the projection step efficiently splits the difficulties brought by the obstacle and the motion by mean curvature of the capillary surface. Furthermore, we prove the unconditional stability of the scheme and present an accuracy check. The convergence of the proposed scheme is also proved using a nonlinear Trotter-Kato's product formula under the pinning contact line assumption. After incorporating the phase transition information at splitting points, several challenging examples including splitting and merging of droplets are demonstrated.Comment: 26 page

Coupled DEM-LBM method for the free-surface simulation of heterogeneous suspensions

The complexity of the interactions between the constituent granular and liquid phases of a suspension requires an adequate treatment of the constituents themselves. A promising way for numerical simulations of such systems is given by hybrid computational frameworks. This is naturally done, when the Lagrangian description of particle dynamics of the granular phase finds a correspondence in the fluid description. In this work we employ extensions of the Lattice-Boltzmann Method for non-Newtonian rheology, free surfaces, and moving boundaries. The models allows for a full coupling of the phases, but in a simplified way. An experimental validation is given by an example of gravity driven flow of a particle suspension

A 3D MHD model of astrophysical flows: algorithms, tests and parallelisation

In this paper we describe a numerical method designed for modelling different kinds of astrophysical flows in three dimensions. Our method is a standard explicit finite difference method employing the local shearing-box technique. To model the features of astrophysical systems, which are usually compressible, magnetised and turbulent, it is desirable to have high spatial resolution and large domain size to model as many features as possible, on various scales, within a particular system. In addition, the time-scales involved are usually wide-ranging also requiring significant amounts of CPU time. These two limits (resolution and time-scales) enforce huge limits on computational capabilities. The model we have developed therefore uses parallel algorithms to increase the performance of standard serial methods. The aim of this paper is to report the numerical methods we use and the techniques invoked for parallelising the code. The justification of these methods is given by the extensive tests presented herein.Comment: 17 pages with 21 GIF figures. Accepted for publication in A&

Numerical investigation of boiling

In this work, we study different phenomena that occur during nucleate boiling. We numerically investigate boiling using two phase flow direct numerical simulation based on a level set / Ghost Fluid method. This method allows us to follow the interface and to make accurate geometric calculation as for bubble curvature. Nucleate boiling on a plate is not only a thermal issue, but also involves multiphase dynamics issues at different scales and at different stages of bubble growth. As a consequence, we divide the whole problem and investigate separately the different phenomena considering their nature and the scale at which they occur. First we analyse the boiling of a static bubble immersed in an overheated liquid. We perform numerical simulations at different Jakob numbers in the case of strong discontinuity of density through the interface. These simulations permit us to estimate the accuracy of our numerical method dealing with phase change in the context of two phase flow direct numerical simulation. The results show a good agreement between numerical bubble radius evolution and the theoretical evolution found by Scriven(1959). The validation of our code for the Scriven case allows to pursue our study by focusing on the phenomena that take place in the particular case of an interaction with a wall. This interaction is characterised by the angle formed between a solid and a fluid interface, named the contact angle. We implement a method that makes it possible for a droplet, to reach, in the case of a static contact angle, a steady state corresponding to a theoretical equilibrium. Besides this method enables to take into account the contact angle hysteresis model, which considers different angles whether the contact line is advancing or recoiling. We perform simulations of the spreading of a liquid droplet impacting on a plate, and we compare the maximum spreading diameter and the advancing and receding droplet behaviour of our numerical results with the experimental data Son and Lee (2010) have reported

Hybrid Spectral Difference/Embedded Finite Volume Method for Conservation Laws

A novel hybrid spectral difference/embedded finite volume method is introduced in order to apply a discontinuous high-order method for large scale engineering applications involving discontinuities in the flows with complex geometries. In the proposed hybrid approach, the finite volume (FV) element, consisting of structured FV subcells, is embedded in the base hexahedral element containing discontinuity, and an FV based high-order shock-capturing scheme is employed to overcome the Gibbs phenomena. Thus, a discontinuity is captured at the resolution of FV subcells within an embedded FV element. In the smooth flow region, the SD element is used in the base hexahedral element. Then, the governing equations are solved by the SD method. The SD method is chosen for its low numerical dissipation and computational efficiency preserving high-order accurate solutions. The coupling between the SD element and the FV element is achieved by the globally conserved mortar method. In this paper, the 5th-order WENO scheme with the characteristic decomposition is employed as the shock-capturing scheme in the embedded FV element, and the 5th-order SD method is used in the smooth flow field. The order of accuracy study and various 1D and 2D test cases are carried out, which involve the discontinuities and vortex flows. Overall, it is shown that the proposed hybrid method results in comparable or better simulation results compared with the standalone WENO scheme when the same number of solution DOF is considered in both SD and FV elements.Comment: 27 pages, 17 figures, 2 tables, Accepted for publication in the Journal of Computational Physics, April 201