Multiresolution Particle Methods for Multiphase Flows – MPARME

The quantification, understanding and prediction of the dynamics of multiphase flows is essential for gaining insight in natural phenomena and for designing engineering devices. Examples range from galaxy formations and volcanic eruptions to solar hydrogen generators and blood separating microchips. We propose the advancement of the knowledge and prediction frontier for multiphase flows through state of the art Direct Numerical Simulation (DNS) made possible by developments in multi-resolution particle methods and their effective deployment on high performance computing (HPC) architectures.

Multiphase flows further extenuate the already stringent requirements for DNS of free-space and wall-bounded separated and turbulent flows. The computational elements have to resolve multiple spatio-temporal scales, handle the physics associated with the different phases, adapt to capture their interfaces and the flow-structure interactions in complex geometries. We will address these challenges by developing four closely interlinked components:
- A unified formulation of particle methods to resolve the evolution of the different phases and their interfaces. The governing Lagrangian equations of motion will be augmented by penalization terms to account for the boundary conditions and transport phenomena across interfaces.
- Novel particle re-meshing algorithms based on wavelet adapted grids. These methods will address inaccuracies due to distorted particles and resolve discontinuities across interfaces.
- Efficient algorithms that translate these methods into software that can harness the power of massively parallel computer architectures.
- Benchmarks to validate our methods and simulations that will help showcase their capabilities and advance our knowledge on the dynamics of multi-phase incompressible flows.

This proposal builds on the strengths and complementarities of our team in the development of particle methods, devising algorithms and software for HPC and in simulating challenging flow physics.

We will develop novel numerical methods, open source software and state of the art DNS of particulate and bubbly flows in complex geometries. We expect to advance knowledge on the role of density and vorticity in the overall dynamics of variable density incompressible flows in laminar and turbulent regimes. Achieving these goals requires that we advance the state of the art in two-phase flow solvers in terms of resolution, memory footprint and time to solution by 2-3 orders of magnitudes. We will employ particles with effective resolutions of O(10^15) computational elements at a fraction of the computational cost of the corresponding uniform grid. Such capability will enable us to study turbulent particulate flows with O(10^{5}) bubbles and particles and explore via DNS unprecedented Reynolds numbers in the order of 10^5. We will produce computational tools that reduce significantly the time to solution for multiphase flow simulations so as to to enable reliable engineering studies.

We expect that the developed particle methodology will find, beyond the applications considered in this project, a number of interdisciplinary applications in scientific fields such as astrophysics and environmental studies dominated by multi-phase flows.