# A priori mesh quality metrics for three-dimensional hybrid grids

## Abstract

Use of general hybrid grids to attain complex-geometry field simulations poses a challenge on estimation of their quality. Apart from the typical problems of non-uniformity and non-orthogonality, the change in element topology is an extra issue to address. The present work derives and evaluates an a priori mesh quality indicator for structured, unstructured, as well as hybrid grids consisting of hexahedra, prisms, tetrahedra, and pyramids. Emphasis is placed on deriving a direct relation between the quality measure and mesh distortion. The work is based on use of the Finite Volume discretization for evaluation of first order spatial derivatives. The analytic form of the truncation error is derived and applied to elementary types of mesh distortion including typical hybrid grid interfaces. The corresponding analytic expressions provide relations between the truncation error and the degree of stretching, skewness, shearing, torsion, expansion, as well as the type of grid interface.

- Authors:

- Publication Date:

- OSTI Identifier:
- 22382163

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Computational Physics; Journal Volume: 280; Other Information: Copyright (c) 2014 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:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMMETRY; COMPUTERIZED SIMULATION; ERRORS; EVALUATION; GEOMETRY; INDICATORS; METRICS; SHEAR; STATISTICS; THREE-DIMENSIONAL CALCULATIONS; TOPOLOGY; TORSION

### Citation Formats

```
Kallinderis, Y., E-mail: kallind@otenet.gr, and Fotia, S., E-mail: soph.fotia@gmail.com.
```*A priori mesh quality metrics for three-dimensional hybrid grids*. United States: N. p., 2015.
Web. doi:10.1016/J.JCP.2014.09.036.

```
Kallinderis, Y., E-mail: kallind@otenet.gr, & Fotia, S., E-mail: soph.fotia@gmail.com.
```*A priori mesh quality metrics for three-dimensional hybrid grids*. United States. doi:10.1016/J.JCP.2014.09.036.

```
Kallinderis, Y., E-mail: kallind@otenet.gr, and Fotia, S., E-mail: soph.fotia@gmail.com. Thu .
"A priori mesh quality metrics for three-dimensional hybrid grids". United States.
doi:10.1016/J.JCP.2014.09.036.
```

```
@article{osti_22382163,
```

title = {A priori mesh quality metrics for three-dimensional hybrid grids},

author = {Kallinderis, Y., E-mail: kallind@otenet.gr and Fotia, S., E-mail: soph.fotia@gmail.com},

abstractNote = {Use of general hybrid grids to attain complex-geometry field simulations poses a challenge on estimation of their quality. Apart from the typical problems of non-uniformity and non-orthogonality, the change in element topology is an extra issue to address. The present work derives and evaluates an a priori mesh quality indicator for structured, unstructured, as well as hybrid grids consisting of hexahedra, prisms, tetrahedra, and pyramids. Emphasis is placed on deriving a direct relation between the quality measure and mesh distortion. The work is based on use of the Finite Volume discretization for evaluation of first order spatial derivatives. The analytic form of the truncation error is derived and applied to elementary types of mesh distortion including typical hybrid grid interfaces. The corresponding analytic expressions provide relations between the truncation error and the degree of stretching, skewness, shearing, torsion, expansion, as well as the type of grid interface.},

doi = {10.1016/J.JCP.2014.09.036},

journal = {Journal of Computational Physics},

number = ,

volume = 280,

place = {United States},

year = {Thu Jan 01 00:00:00 EST 2015},

month = {Thu Jan 01 00:00:00 EST 2015}

}