Sharp Collocated Projection Method for Immiscible Two-Phase Flows

TL;DR

This paper introduces a high-accuracy, sharp collocated projection method for simulating immiscible two-phase flows using adaptive quadtree and octree grids, with novel discretizations for boundary and interface conditions.

Contribution

The paper presents a new collocated projection method with hybrid discretizations on adaptive grids for improved accuracy in two-phase flow simulations.

Findings

Achieves high accuracy in 2D and 3D flow simulations.

Employs a hybrid finite difference-finite volume approach.

Demonstrates effectiveness on canonical examples.

Abstract

We present a sharp collocated projection method for solving the immiscible, two-phase Navier-Stokes equations in two- and three-dimensions. Our method is built using non-graded adaptive quadtree and octree grids, where all of the fluid variables are defined on the nodes, and we leverage this framework to design novel spatial and temporal discretizations for the two-phase problem. The benefits of the nodal collocation framework are best exemplified through our novel discretizations, which employ a hybrid finite difference-finite volume methodology to treat the boundary and interfacial jump conditions in an entirely sharp manner. We demonstrate the capabilities of our novel approach using a variety of canonical two- and three-dimensional examples and outline how our framework can be extended to address more complicated physics. The overall algorithm achieves high accuracy with simplified data structures, making this solver ideal for scientific and engineering applications.