## Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach

## Abstract

Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, *P*, promotion is used to extend the low-order *P* = 1 CVFEM method to higher-order, i.e., *P* = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.

- Authors:

- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

- Sponsoring Org.:
- USDOE Office of Science (SC)

- OSTI Identifier:
- 1465806

- Report Number(s):
- SAND-2017-10354J

Journal ID: ISSN 0021-9991; 666503; TRN: US1902560

- Grant/Contract Number:
- AC04-94AL85000

- Resource Type:
- Accepted Manuscript

- Journal Name:
- Journal of Computational Physics

- Additional Journal Information:
- Journal Volume: 359; Journal Issue: C; Journal ID: ISSN 0021-9991

- Publisher:
- Elsevier

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Control volume finite element; Discontinuous Galerkin; Higher-order; Sliding mesh; Non-conformal

### Citation Formats

```
Domino, Stefan P. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. United States: N. p., 2018.
Web. doi:10.1016/j.jcp.2018.01.007.
```

```
Domino, Stefan P. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. United States. doi:10.1016/j.jcp.2018.01.007.
```

```
Domino, Stefan P. Fri .
"Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach". United States. doi:10.1016/j.jcp.2018.01.007. https://www.osti.gov/servlets/purl/1465806.
```

```
@article{osti_1465806,
```

title = {Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach},

author = {Domino, Stefan P.},

abstractNote = {Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P, promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.},

doi = {10.1016/j.jcp.2018.01.007},

journal = {Journal of Computational Physics},

number = C,

volume = 359,

place = {United States},

year = {2018},

month = {1}

}

*Citation information provided by*

Web of Science

Web of Science