# A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows

## Abstract

In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.

- Authors:

- Mechanical and Industrial Engineering, Montana State University, Bozeman, MT 59717 (United States)
- Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853 (United States)

- Publication Date:

- OSTI Identifier:
- 22622258

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 332; Other Information: Copyright (c) 2016 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ACCURACY; ADVECTION; COMPUTERIZED SIMULATION; CONVECTION; DENSITY; INTERFACES; LAGRANGIAN FUNCTION; LIQUID FLOW; LIQUIDS; MODIFICATIONS; MULTIPHASE FLOW; RESOLUTION; THREE-DIMENSIONAL CALCULATIONS; VERIFICATION

### Citation Formats

```
Owkes, Mark, E-mail: mark.owkes@montana.edu, and Desjardins, Olivier.
```*A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows*. United States: N. p., 2017.
Web. doi:10.1016/J.JCP.2016.11.046.

```
Owkes, Mark, E-mail: mark.owkes@montana.edu, & Desjardins, Olivier.
```*A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows*. United States. doi:10.1016/J.JCP.2016.11.046.

```
Owkes, Mark, E-mail: mark.owkes@montana.edu, and Desjardins, Olivier. Wed .
"A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows". United States.
doi:10.1016/J.JCP.2016.11.046.
```

```
@article{osti_22622258,
```

title = {A mass and momentum conserving unsplit semi-Lagrangian framework for simulating multiphase flows},

author = {Owkes, Mark, E-mail: mark.owkes@montana.edu and Desjardins, Olivier},

abstractNote = {In this work, we present a computational methodology for convection and advection that handles discontinuities with second order accuracy and maintains conservation to machine precision. This method can transport a variety of discontinuous quantities and is used in the context of an incompressible gas–liquid flow to transport the phase interface, momentum, and scalars. The proposed method provides a modification to the three-dimensional, unsplit, second-order semi-Lagrangian flux method of Owkes & Desjardins (JCP, 2014). The modification adds a refined grid that provides consistent fluxes of mass and momentum defined on a staggered grid and discrete conservation of mass and momentum, even for flows with large density ratios. Additionally, the refined grid doubles the resolution of the interface without significantly increasing the computational cost over previous non-conservative schemes. This is possible due to a novel partitioning of the semi-Lagrangian fluxes into a small number of simplices. The proposed scheme is tested using canonical verification tests, rising bubbles, and an atomizing liquid jet.},

doi = {10.1016/J.JCP.2016.11.046},

journal = {Journal of Computational Physics},

number = ,

volume = 332,

place = {United States},

year = {Wed Mar 01 00:00:00 EST 2017},

month = {Wed Mar 01 00:00:00 EST 2017}

}