Accurate and Efficient Coupled Surfactant Calculations for Two-Phase Flows with the Discrete Exterior Calculus

In this project, we will develop a new, robust, accurate and GPU-parallelized solver for two-phase flow problems with surfactants on the free surface. Based on our existing solver NaSt3DGPF, we will apply an explicit mesh construction method
for the fluid/fluid interface which performs smooth sub-cell sampling in a generalization of the marching cubes algorithm.

Figures: preliminary work in interface tracking / mass conservation with NaSt3DGPF

Figure: Commutative diagram of the operators mapping between primal and dual mesh and different simplices in DEC

Figure: Overall scheme of the applied couplings and techniques

Figures: preliminary work in interface tracking / mass conservation with NaSt3DGPF

A key feature is then the Discrete Exterior Calculus (DEC) which will be employed on the interface mesh for the numercial treatment of the surfactant-PDE, the calculation of the surface tension and the coupling of the interface-PDE to the bulk equations with significantly different densities. Together with a sharp interface capturing bulk discretization, DEC promises to obtain stability, robustness and improved accuracy for the surfactant equations on the interface, the surface tension calculations and the bulk quantities even close to the interface.

Figure: Commutative diagram of the operators mapping between primal and dual mesh and different simplices in DEC

We furthermore will parallelize the new approach for a cluster of GPU compute nodes to obtain a fast simulation tool for (Taylor) bubble problems and droplet breakup in shear driven flows in the presence of surfactants.

Figure: Overall scheme of the applied couplings and techniques