The Development of High-Order Interface Tracking Schemes for the Simulation of Multiphase Flows

Bryce Campbell | 18-ERD-053

Project Overview

Multi-fluid flows are an important field within the study of fluid mechanics, and the simultaneous presence of more than one fluid enables these flows to exist in a large range of flow regimes. However, the resulting fluid dynamics display complex, multiscale physical characteristics that are difficult to simulate accurately using existing low-order methods. Typically, multiphase simulation algorithms consist of two components: (1) a method for tracking the interface between the phases, and (2) a method that solves the mass, momentum, and energy equations. In our project, we focused on developing high-order numerical algorithms for the simulation of coupled multiphase flows.

We developed a novel, arbitrarily high-order, Cartesian-grid method for reconstructing and tracking material interfaces from a volume fraction field. The method involves identifying all of the interfacial grid cells and decomposing these interfacial grid cells into a series of patches. Using an integral constraint, these grid cells are coupled together and used to approximate the interface as high-order (Nth-order polynomial) curve or tensor-product surface. We demonstrated that fitting the surface with an Nth-order curve or surface yields an (N-1)th-order convergence rate of the interface shape. Additionally, a two-dimensional fluid advection algorithm was developed, which moves the interface in response to an ambient velocity field. This method retains the same high-order convergence rate as the reconstruction algorithm and can be made to be area conserving to within machine precision accuracy. The method was rigorously validated and was demonstrated to be highly efficient and scalable on parallel systems.

Such an algorithm can help lead to dramatic increases in solution accuracy, lower computational costs, allow for the direct simulation of significantly more complex engineering flows and do so without requiring the mesh to conform to the fluid interface (as is required by most finite element methods). The generality and increased accuracy provided by the proposed algorithms makes this method directly applicable to a broad range of science and engineering disciplines. For example, this new code capability will have applications in the investigation of inertial-confinement fusion, turbulent mixing, flow instability, and fluid interactions with elastic-plastic structures.

Mission Impact

The algorithms and methods developed in this project directly support Lawrence Livermore National Laboratory's core competency in high-performance computing, simulation, and data science. The methods are fast and highly scalable onto large parallel computing platforms. In addition, the methods may help improve the direct simulation of complex physical problems, such as inertial confinement fusion; compressible multiphase flows; surface tension dominated flows; oceanic air-sea interactions; and rapid prototyping of micro-fluidics. The methods we developed will also support the general pursuit of direct numerical simulations of stronger turbulent multiphase flows.

Publications, Presentations, and Patents

Campbell, B. 2019. "A Fast Multi-Layer Boundary Element Method for Direct Numerical Simulation of Sound Propagation in Shallow Water Environments." Journal of Computational Physics, 392, 694–712. LLNL-JRNL-767818

——— 2019. "An Arbitrarily High-Order, Conservative, Cartesian-Grid Interface Tracking Scheme for Multiphase Flow Simulations." International Conference on Multiphase Flow, Rio de Janeiro, Brazil, May 2019. LLNL-PRES-774231

——— 2021. "An arbitrarily high-order three-dimensional Cartesian-grid method for reconstructing interfaces from volume fraction fields." Journal of Computational Physics, doi:10.1016/ LLNL-JRNL-796117