# Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)

## Abstract

In recent work (Nourgaliev, Liou, Theofanous, JCP in press) we demonstrated that numerical simulations of interfacial flows in the presence of strong shear must be cast in dynamically sharp terms (sharp interface treatment or SIM), and that moreover they must meet stringent resolution requirements (i.e., resolving the critical layer). The present work is an outgrowth of that work aiming to overcome consequent limitations on the temporal treatment, which become still more severe in the presence of phase change. The key is to avoid operator splitting between interface motion, fluid convection, viscous/heat diffusion and reactions; instead treating all these non-linear operators fully-coupled within a Newton iteration scheme. To this end, the SIM’s cut-cell meshing is combined with the high-orderaccurate implicit Runge-Kutta and the “recovery” Discontinuous Galerkin methods along with a Jacobian-free, Krylov subspace iteration algorithm and its physics-based preconditioning. In particular, the interfacial geometry (i.e., marker’s positions and volumes of cut cells) is a part of the Newton-Krylov solution vector, so that the interface dynamics and fluid motions are fully-(non-linearly)-coupled. We show that our method is: (a) robust (L-stable) and efficient, allowing to step over stability time steps at will while maintaining high-(up to the 5th)-order temporal accuracy; (b) fully conservative,more »

- Authors:

- Publication Date:

- Research Org.:
- Idaho National Laboratory (INL)

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 927623

- Report Number(s):
- INL/CON-08-13676

TRN: US0804800

- DOE Contract Number:
- DE-AC07-99ID-13727

- Resource Type:
- Conference

- Resource Relation:
- Conference: American Institute of Aeronautics and Astronautics,Reno, NV,01/07/2008,01/10/2008

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 22 GENERAL STUDIES OF NUCLEAR REACTORS; ACCURACY; ALGORITHMS; CONVECTION; DIFFUSION; GEOMETRY; OSCILLATIONS; PERFORMANCE; RESOLUTION; SHEAR; SIMULATION; STABILITY; VELOCITY; Multiphysics

### Citation Formats

```
Nourgaliev, Robert, Theofanous, Theo, Park, HyeongKae, Mousseau, Vincent, and Knoll, Dana.
```*Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)*. United States: N. p., 2008.
Web. doi:10.2514/6.2008-1453.

```
Nourgaliev, Robert, Theofanous, Theo, Park, HyeongKae, Mousseau, Vincent, & Knoll, Dana.
```*Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)*. United States. doi:10.2514/6.2008-1453.

```
Nourgaliev, Robert, Theofanous, Theo, Park, HyeongKae, Mousseau, Vincent, and Knoll, Dana. Tue .
"Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)". United States. doi:10.2514/6.2008-1453. https://www.osti.gov/servlets/purl/927623.
```

```
@article{osti_927623,
```

title = {Direct Numerical Simulation of Interfacial Flows: Implicit Sharp-Interface Method (I-SIM)},

author = {Nourgaliev, Robert and Theofanous, Theo and Park, HyeongKae and Mousseau, Vincent and Knoll, Dana},

abstractNote = {In recent work (Nourgaliev, Liou, Theofanous, JCP in press) we demonstrated that numerical simulations of interfacial flows in the presence of strong shear must be cast in dynamically sharp terms (sharp interface treatment or SIM), and that moreover they must meet stringent resolution requirements (i.e., resolving the critical layer). The present work is an outgrowth of that work aiming to overcome consequent limitations on the temporal treatment, which become still more severe in the presence of phase change. The key is to avoid operator splitting between interface motion, fluid convection, viscous/heat diffusion and reactions; instead treating all these non-linear operators fully-coupled within a Newton iteration scheme. To this end, the SIM’s cut-cell meshing is combined with the high-orderaccurate implicit Runge-Kutta and the “recovery” Discontinuous Galerkin methods along with a Jacobian-free, Krylov subspace iteration algorithm and its physics-based preconditioning. In particular, the interfacial geometry (i.e., marker’s positions and volumes of cut cells) is a part of the Newton-Krylov solution vector, so that the interface dynamics and fluid motions are fully-(non-linearly)-coupled. We show that our method is: (a) robust (L-stable) and efficient, allowing to step over stability time steps at will while maintaining high-(up to the 5th)-order temporal accuracy; (b) fully conservative, even near multimaterial contacts, without any adverse consequences (pressure/velocity oscillations); and (c) highorder-accurate in spatial discretization (demonstrated here up to the 12th-order for smoothin-the-bulk-fluid flows), capturing interfacial jumps sharply, within one cell. Performance is illustrated with a variety of test problems, including low-Mach-number “manufactured” solutions, shock dynamics/tracking with slow dynamic time scales, and multi-fluid, highspeed shock-tube problems. We briefly discuss preconditioning, and we introduce two physics-based preconditioners – “Block-Diagonal” and “Internal energy-Pressure-Velocity Partially Decoupled”, demonstrating the ability to efficiently solve all-speed flows with strong effects from viscous dissipation and heat conduction.},

doi = {10.2514/6.2008-1453},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2008},

month = {1}

}