# Notes on Newton-Krylov based Incompressible Flow Projection Solver

## Abstract

The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.

- Authors:

- Publication Date:

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

- Sponsoring Org.:
- DOE - NE

- OSTI Identifier:
- 1058093

- Report Number(s):
- INL/EXT-12-27197

- DOE Contract Number:
- DE-AC07-05ID14517

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; Projection method, Fluid dynamics, thermalhydrauli

### Citation Formats

```
Robert Nourgaliev, Mark Christon, and J. Bakosi.
```*Notes on Newton-Krylov based Incompressible Flow Projection Solver*. United States: N. p., 2012.
Web. doi:10.2172/1058093.

```
Robert Nourgaliev, Mark Christon, & J. Bakosi.
```*Notes on Newton-Krylov based Incompressible Flow Projection Solver*. United States. doi:10.2172/1058093.

```
Robert Nourgaliev, Mark Christon, and J. Bakosi. Sat .
"Notes on Newton-Krylov based Incompressible Flow Projection Solver". United States. doi:10.2172/1058093. https://www.osti.gov/servlets/purl/1058093.
```

```
@article{osti_1058093,
```

title = {Notes on Newton-Krylov based Incompressible Flow Projection Solver},

author = {Robert Nourgaliev and Mark Christon and J. Bakosi},

abstractNote = {The purpose of the present document is to formulate Jacobian-free Newton-Krylov algorithm for approximate projection method used in Hydra-TH code. Hydra-TH is developed by Los Alamos National Laboratory (LANL) under the auspices of the Consortium for Advanced Simulation of Light-Water Reactors (CASL) for thermal-hydraulics applications ranging from grid-to-rod fretting (GTRF) to multiphase flow subcooled boiling. Currently, Hydra-TH is based on the semi-implicit projection method, which provides an excellent platform for simulation of transient single-phase thermalhydraulics problems. This algorithm however is not efficient when applied for very slow or steady-state problems, as well as for highly nonlinear multiphase problems relevant to nuclear reactor thermalhydraulics with boiling and condensation. These applications require fully-implicit tightly-coupling algorithms. The major technical contribution of the present report is the formulation of fully-implicit projection algorithm which will fulfill this purpose. This includes the definition of non-linear residuals used for GMRES-based linear iterations, as well as physics-based preconditioning techniques.},

doi = {10.2172/1058093},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2012},

month = {9}

}