# Interfacing MFIX with PETSC and HYPRE Linear Solver Libraries: Final Report

## Abstract

A computational bottleneck during the solution to multiphase formulations of the incompressible Navier-Stokes equations is often during the implicit solution of the pressure correction equation that results from operator-splitting methods. Since density is a coefficient in the pressure-correction equation, large variations or discontinuities among the phase densities greatly increase the condition number of the pressure-correction matrix and retard the convergence of iterative methods employed in its solution. To alleviate this shortcoming, the open-source multiphase code MFiX is interfaced with the linear solver libraries PETSc and HYPRE. Through an appropriate mapping of matrix and vector data structures between the two software packages, an access to a suite of robust, scalable, solver options in PETSc and HYPRE is obtained. Verification of the implementation is demonstrated through predictions that are identical to those obtained from MFiX’s native solvers for a class of single-phase and multiphase flow problems.

- Authors:

- Publication Date:

- Research Org.:
- Univ. of North Dakota, Grand Forks, ND (United States)

- Sponsoring Org.:
- USDOE Office of Fossil Energy (FE)

- OSTI Identifier:
- 1592576

- Report Number(s):
- Final Report: DOE-UND-0026191

- DOE Contract Number:
- FE0026191

- Resource Type:
- Technical Report

- Resource Relation:
- Related Information: Clarke, Lauren Elizabeth, and Gautham Krishnamoorthy. "Pre-conditioning strategies to accelerate the convergence of iterative methods in multiphase flow simulations." Mathematics and Computers in Simulation, Volume 165, November 2019, Pages 200-222Clarke, Lauren Elizabeth, "Interfacing The CFD Code MFiX With The PETSc Linear Solver Library To Achieve Reduced Computation Times," MS Thesis, University of North Dakota, January 2018

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 97 MATHEMATICS AND COMPUTING; CFD; PETSc; HYPRE; MFiX; BiCGSTAB; Multiphase flow

### Citation Formats

```
Krishnamoorthy, Gautham, and Thornock, Jeremy.
```*Interfacing MFIX with PETSC and HYPRE Linear Solver Libraries: Final Report*. United States: N. p., 2020.
Web. doi:10.2172/1592576.

```
Krishnamoorthy, Gautham, & Thornock, Jeremy.
```*Interfacing MFIX with PETSC and HYPRE Linear Solver Libraries: Final Report*. United States. doi:10.2172/1592576.

```
Krishnamoorthy, Gautham, and Thornock, Jeremy. Tue .
"Interfacing MFIX with PETSC and HYPRE Linear Solver Libraries: Final Report". United States. doi:10.2172/1592576. https://www.osti.gov/servlets/purl/1592576.
```

```
@article{osti_1592576,
```

title = {Interfacing MFIX with PETSC and HYPRE Linear Solver Libraries: Final Report},

author = {Krishnamoorthy, Gautham and Thornock, Jeremy},

abstractNote = {A computational bottleneck during the solution to multiphase formulations of the incompressible Navier-Stokes equations is often during the implicit solution of the pressure correction equation that results from operator-splitting methods. Since density is a coefficient in the pressure-correction equation, large variations or discontinuities among the phase densities greatly increase the condition number of the pressure-correction matrix and retard the convergence of iterative methods employed in its solution. To alleviate this shortcoming, the open-source multiphase code MFiX is interfaced with the linear solver libraries PETSc and HYPRE. Through an appropriate mapping of matrix and vector data structures between the two software packages, an access to a suite of robust, scalable, solver options in PETSc and HYPRE is obtained. Verification of the implementation is demonstrated through predictions that are identical to those obtained from MFiX’s native solvers for a class of single-phase and multiphase flow problems.},

doi = {10.2172/1592576},

journal = {},

number = ,

volume = ,

place = {United States},

year = {2020},

month = {1}

}