### Abstract

Code verification answers the question: " Is this code solving the equations correctly?" Validation answers the question: " Is this code solving the correct equations?" Code verification must be performed before attempting validation and is the focus of this paper. Here we present a novel method of applying the method of manufactured solutions (MMS) to finite volume multiphase codes. MMS is a procedure for generating analytic source terms and adding them to the governing equations such that the numerical solution converges to a previously determined analytic (manufactured) solution. This is a powerful method for generating exact benchmark solutions which can test the most general capabilities of a code. We present a series of manufactured solutions (MS) ranging from single-phase to multiphase flows to test all aspects of an example code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented here using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. We also present guidelines for the use of the MMS to help locate coding mistakes (i.e. bugs). This is accomplished by the use of progressively simpler MS and material property variations.

Original language | English (US) |
---|---|

Pages (from-to) | 2924-2944 |

Number of pages | 21 |

Journal | Journal of Computational Physics |

Volume | 231 |

Issue number | 7 |

DOIs | |

State | Published - Apr 1 2012 |

### Fingerprint

### Keywords

- Code verification
- Finite volume
- Level set
- Manufactured solutions
- Multiphase
- Numerical methods

### ASJC Scopus subject areas

- Computer Science Applications
- Physics and Astronomy (miscellaneous)

### Cite this

**Code verification for finite volume multiphase scalar equations using the method of manufactured solutions.** / Brady, P. T.; Herrmann, Marcus; Lopez, Juan.

Research output: Contribution to journal › Article

*Journal of Computational Physics*, vol. 231, no. 7, pp. 2924-2944. https://doi.org/10.1016/j.jcp.2011.12.040

}

TY - JOUR

T1 - Code verification for finite volume multiphase scalar equations using the method of manufactured solutions

AU - Brady, P. T.

AU - Herrmann, Marcus

AU - Lopez, Juan

PY - 2012/4/1

Y1 - 2012/4/1

N2 - Code verification answers the question: " Is this code solving the equations correctly?" Validation answers the question: " Is this code solving the correct equations?" Code verification must be performed before attempting validation and is the focus of this paper. Here we present a novel method of applying the method of manufactured solutions (MMS) to finite volume multiphase codes. MMS is a procedure for generating analytic source terms and adding them to the governing equations such that the numerical solution converges to a previously determined analytic (manufactured) solution. This is a powerful method for generating exact benchmark solutions which can test the most general capabilities of a code. We present a series of manufactured solutions (MS) ranging from single-phase to multiphase flows to test all aspects of an example code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented here using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. We also present guidelines for the use of the MMS to help locate coding mistakes (i.e. bugs). This is accomplished by the use of progressively simpler MS and material property variations.

AB - Code verification answers the question: " Is this code solving the equations correctly?" Validation answers the question: " Is this code solving the correct equations?" Code verification must be performed before attempting validation and is the focus of this paper. Here we present a novel method of applying the method of manufactured solutions (MMS) to finite volume multiphase codes. MMS is a procedure for generating analytic source terms and adding them to the governing equations such that the numerical solution converges to a previously determined analytic (manufactured) solution. This is a powerful method for generating exact benchmark solutions which can test the most general capabilities of a code. We present a series of manufactured solutions (MS) ranging from single-phase to multiphase flows to test all aspects of an example code. The chief obstacle to applying MMS to multiphase flow lies in the discontinuous nature of the material properties at the interface. An extension of the MMS procedure to multiphase flow is presented here using an adaptive marching tetrahedron style algorithm to compute the source terms near the interface. We also present guidelines for the use of the MMS to help locate coding mistakes (i.e. bugs). This is accomplished by the use of progressively simpler MS and material property variations.

KW - Code verification

KW - Finite volume

KW - Level set

KW - Manufactured solutions

KW - Multiphase

KW - Numerical methods

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U2 - 10.1016/j.jcp.2011.12.040

DO - 10.1016/j.jcp.2011.12.040

M3 - Article

AN - SCOPUS:84856583058

VL - 231

SP - 2924

EP - 2944

JO - Journal of Computational Physics

JF - Journal of Computational Physics

SN - 0021-9991

IS - 7

ER -