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Energy stable numerical schemes for simulating two-phase flows by solving Cahn-Hilliard Navier Stokes equations on adaptive octree meshes

Event Type: 
Date and Time: 
Friday, November 5, 2021 - 16:15
Building 300, Room 300
Event Sponsor: 
Parviz Moin, Director of Center for Turbulence Research
Dr. Makrand Khanwale

Developing accurate, stable, and thermodynamically consistent numerical methods to simulate two-phase flows is critical for many applications. We develop numerical methods to solve thermodynamically consistent Cahn-Hilliard Navier-Stokes equations to simulate two-phase flows with deforming interfaces at various density contrasts. We develop three essentially unconditionally energy-stable time integration schemes. The first two time-integration schemes are fully implicit based on the pressure-stabilization technique. The third approach utilizes the projection method to decouple the pressure to improve the efficiency of the fully implicit scheme.  We rigorously prove the energy stability of the time-discrete numerical schemes for the approaches with pressure-stabilization approaches. We also prove the existence of solutions of the advective-diffusive Cahn-Hilliard operator.  We use a conforming continuous Galerkin (CG) finite element method in space equipped with a residual-based variational multiscale (RBVMS) procedure to stabilize the pressure in the first two approaches. In the third approach, we present a projection based framework extending the fully implicit method to a block iterative, hybrid semi-implicit-fully-implicit in time method.  We use a semi-implicit time discretization for Navier-Stokes and a fully-implicit time discretization for Cahn-Hilliard equations.  Pressure is decoupled using a projection step resulting in two linear positive semi-definite systems for velocity and pressure instead of the saddle point system of a pressure-stabilized method.  All the resulting linear systems are solved using the efficient and scalable algebraic multigrid (AMG) method. We deploy all three approaches on a massively parallel numerical implementation using fast octree-based adaptive meshes in a computational framework called "Proteus". We perform a detailed scaling analysis of all three solvers.  A comprehensive set of numerical experiments showing detailed comparisons with results from the literature for canonical cases are used to validate the methods for an extensive range of density ratios. This presentation is an overview of the main developments of Khanwale's PhD research. Khanwale will also discuss his plans to push the boundaries of phase-field methods and develop robust multiphysics solvers which couple scalar transport, electroconvection with multiphase flows.

Dr. Makrand Ajay Khanwale is currently a Postdoctoral Fellow at the Center for Turbulence Research at Stanford University. He received his PhD in the Summer of 2021 from Iowa State University (ISU), co-majoring in Mechanical Engineering and Applied Mathematics. At ISU, he was co-advised by Dr. Baskar Ganapathysubramanian and Dr. James Rossmanith. For his dissertation, he worked on developing and analysing numerical schemes for high fidelity simulations of multiphase flows. Specifically, he developed energy stable numerical methods to simulate two-phase flows using Cahn-Hilliard Navier-Stokes equations. Before joining Iowa State for his graduate work, he had a brief stint as a research associate in Dr. Krishnaswamy Nandakumar‘s group at Louisiana State University (LSU). At LSU, he worked on developing closure models for energy cascades in multiphase flows. He received his Bachelors in Chemical Technology from the Institute of Chemical Technology, Mumbai.