Marianne M Francois

We present a method to simulate surface tension between immiscible materials within an inviscid compressible flow solver. The material interface is represented using the volume of fluid technique with piecewise-linear interface reconstruction. We employ the continuum surface force model for surface tension, implemented in the context of the MUSCL-Hancock finite volume method for the Euler equations on an adaptively refined Eulerian mesh. We show results for droplet verification test cases.

We focus on the simulation of shock-driven. material mixing powered by flow instabilities dependent on initial conditions (IC) at the material interfaces. Beyond complex multi-scale resolution issues of shocks and variable density turbulence, we must address the equally difficult problem of predicting flow transition promoted by energy deposited at the interfacial layers during the shock-interface interactions. Transition involves IC dependent, large-scale coherent-structure dynamics capturable by a large eddy simulation (LES) strategy, but not by unsteady Reynolds-Averaged Navier-Stokes (URANS) approaches based on equilibrium developed turbulence assumptions and single point-closure modeling. On the engineering end of computations, reduced-dimensionality (1D/2D) versions of such URANS tend to be preferred for faster turnaround in full-scale configurations. With suitable initialization around each transition, URANS can be used to simulate the subsequent near-equilibrium weakly turbulent flow. We demonstrate 3D state-of-the-art URANS performance around one such (reshock) transition in the context of a sequential LES/URANS strategy.

With the increasing heterogeneity and on-node parallelism of high-performance computing hardware, a major challenge to computational physicists is to work in close collaboration with computer scientists to develop portable and efficient algorithms and software. The objective of our work is to implement a portable code to perform interface reconstruction using NVIDIA's Thrust library. Interface reconstruction is a technique commonly used in volume tracking methods for simulations of interfacial flows. For that, we have designed a two-dimensional mesh data structure that is easily mapped to the 1D vectors used by Thrust and at the same time is simple to work with using familiar data structures terminology (such as cell, vertices and edges). With this new data structure in place, we have implemented a recursive volume-of-fluid initialization algorithm and a standard piecewise interface reconstruction algorithm. Our interface reconstruction algorithm makes use of a table look-up to easily identify all intersection cases, as this design is efficient on parallel architectures such as GPUs. Finally, we report performance results which show that a single implementation of these algorithms can be compiled to multiple backends (specifically, multi-core CPUs, NVIDIA GPUs, and Intel Xeon Phi coprocessors), making efficient use of the available parallelism on each.

Understanding the complex interaction of droplet dynamics with mass transfer and chemical reactions is of fundamental importance in liquid-liquid extraction. High-fidelity numerical simulation of droplet dynamics with interfacial mass transfer is particularly challenging because the position of the interface between the fluids and the interface physics need to be predicted as part of the solution of the flow equations. In addition, the discontinuity in fluid density, viscosity and species concentration at the interface present additional numerical challenges. In this work, we extend our balanced-force volume-tracking algorithm for modeling surface tension force (Francois et al., 2006) and we propose a global embedded interface formulation to model the interfacial conditions of an interface in thermodynamic equilibrium. To validate our formulation, we perform simulations of pure diffusion problems in one- and two-dimensions. Then we present two and three-dimensional simulations of a single droplet dynamics rising by buoyancy with mass transfer.

Volume tracking method, also referred to as the volume-of-fluid (VOF) method introduces "numerical surface tension" that breaks a filament into a series of droplets whenever the filament is under-resolved. Adaptive mesh refinement can help avoid under-resolution, but a folly-developed flow will still generate filaments that cannot be resolved without enormous computational cost. We propose a complementary new approach that consists of transitioning to a continuous interface representation (i.e. Without interface reconstruction) in regions of under-resolved interfacial curvature where volume tracking has become erroneous. The price of the continuous interface treatment is a small amount of numerical mass diffusion, even if the physical interface is immiscible. However, we have found that for certain measures, the overall accuracy is greatly improved by using our transitioning algorithm. The algorithm is developed in the context of the single fluid formulation of the incompressible Navier-Stokes equations. Numerical standard vortices advection test cases and Rayleigh-Taylor instability computations arc presented to illustrate the transition algorithm potential.