# Aria 1.5 : user manual.

## Abstract

Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picard's method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based on the Sierra Framework.

- Authors:

- Publication Date:

- Research Org.:
- Sandia National Laboratories

- Sponsoring Org.:
- USDOE

- OSTI Identifier:
- 922079

- Report Number(s):
- SAND2007-2734

TRN: US200806%%49

- DOE Contract Number:
- AC04-94AL85000

- Resource Type:
- Technical Report

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 GENERAL AND MISCELLANEOUS//MATHEMATICS, COMPUTING, AND INFORMATION SCIENCE; A CODES; FINITE ELEMENT METHOD; NONLINEAR PROBLEMS; NAVIER-STOKES EQUATIONS; ENERGY TRANSFER; MECHANICS; ELECTROSTATICS; Galerkin methods.; Physics-Computer programs.; Coupled problems (Complex systems)-Mathematical models.

### Citation Formats

```
Hopkins, Matthew Morgan, Moffat, Harry K, Noble, David R, Notz, Patrick K, and Subia, Samuel Ramirez.
```*Aria 1.5 : user manual.*. United States: N. p., 2007.
Web. doi:10.2172/922079.

```
Hopkins, Matthew Morgan, Moffat, Harry K, Noble, David R, Notz, Patrick K, & Subia, Samuel Ramirez.
```*Aria 1.5 : user manual.*. United States. doi:10.2172/922079.

```
Hopkins, Matthew Morgan, Moffat, Harry K, Noble, David R, Notz, Patrick K, and Subia, Samuel Ramirez. Sun .
"Aria 1.5 : user manual.". United States.
doi:10.2172/922079. https://www.osti.gov/servlets/purl/922079.
```

```
@article{osti_922079,
```

title = {Aria 1.5 : user manual.},

author = {Hopkins, Matthew Morgan and Moffat, Harry K and Noble, David R and Notz, Patrick K and Subia, Samuel Ramirez},

abstractNote = {Aria is a Galerkin finite element based program for solving coupled-physics problems described by systems of PDEs and is capable of solving nonlinear, implicit, transient and direct-to-steady state problems in two and three dimensions on parallel architectures. The suite of physics currently supported by Aria includes the incompressible Navier-Stokes equations, energy transport equation, species transport equations, nonlinear elastic solid mechanics, and electrostatics as well as generalized scalar, vector and tensor transport equations. Additionally, Aria includes support for arbitrary Lagrangian-Eulerian (ALE) and level set based free and moving boundary tracking. Coupled physics problems are solved in several ways including fully-coupled Newton's method with analytic or numerical sensitivities, fully-coupled Newton-Krylov methods, fully-coupled Picard's method, and a loosely-coupled nonlinear iteration about subsets of the system that are solved using combinations of the aforementioned methods. Error estimation, uniform and dynamic h-adaptivity and dynamic load balancing are some of Aria's more advanced capabilities. Aria is based on the Sierra Framework.},

doi = {10.2172/922079},

journal = {},

number = ,

volume = ,

place = {United States},

year = {Sun Apr 01 00:00:00 EDT 2007},

month = {Sun Apr 01 00:00:00 EDT 2007}

}