B06: Higher Order Schemes for Direct Numerical Simulation for Wetting and De-Wetting Problems based on Discontinuous Galerkin Methods

Image: Florian Kummer
Image: Florian Kummer

Existing high accuracy discontinuous Galerkin methods for multi-phase flows will be extended to accommodate effects encountered at dynamic contact lines. Focus will be placed on the numerical realization of the slip boundary condition close to the contact line in the DG level-set method. The initial development will be in the framework of the in-house BoSSS (Bounded Support Spectral Solver) code, but will be successively ported to the OpenFOAM environment. With that, a selection of coupled transport and wetting scenarios from the generic configurations will be investigated numerically, in the longer term also including the transport of surfactant and heat transfer near the contact line.

Due to its inherent approximation properties, the DG method shows great potential for the simulation of contact line problems. In the conventional DG-method, polynomial ansatz-functions are used for the approximation of variables like velocity or pressure in each cell. Since discontinuities at the cell boundaries are explicitly allowed, it is not required to use exclusively polynomials. Indeed, one is free to choose other, non-polynomial functions for the approximation of the flow properties. This is especially useful for the integration of sub-scale-models, like the ones used to describe moving contact lines.

Furthermore, the DG-method has proven to be very useful in the context of level-set-methods. Firstly, DG is very suitable for the treatment of convectional processes, as the ones which appear in level-set-methods. Secondly, the position of the fluid interface (i.e. the zero-level-set) can be reconstructed very accurately due to the polynomial nature of the representation, without any artificial interpolation assumptions.