# 1.1. Introduction

The SIERRA Multimechanics Module: Aria, henceforth referred to as Aria for brevity, is an application implementing the finite element method (FEM) for solving systems of partial differential equations (PDEs). Foremost, Aria’s development targets applications which involve incompressible flow (Navier-Stokes for < 1). However, the general design of Aria lends itself to the solution of systems of PDEs describing physical processes including energy transport, species transport with reactions, electrostatics and general transport of scalar, vector and tensor quantities in two and three dimensions both transient and direct to steady state. Moreover, different regions of the physical domain (i.e., the input mesh) may have either different materials and/or different collections of physics (viz., PDEs) defined on them. These systems of equations may be solved alone, in a segregated but coupled algorithm (“loosely coupled”) or as a single, fully-coupled (“monolithic”) system. Additionally, Aria can be loosely coupled to the quasi-statics solid mechanics code Adagio using the coupling application Arpeggio.

Aria is able to accommodate meshes that utilize linear and quadratic elements in two and three dimensions. In two dimensions, Aria supports quadrilateral (4 and 9 node) and triangular (3 and 6 node) elements. In three dimensions, Aria supports hexahedral (8 and 27 node) and tetrahedral (4 and 10 node) elements. Moreover, meshes may be comprised of combinations of these elements (i.e., both quadrilateral and triangular elements in two dimensions).

The physical coordinates and mesh displacements are always interpolated in accordance with the input mesh, but other solution degrees of freedom may be interpolated using a lower order basis function. For example, if the input mesh is composed of 9 node (quadratic) quadrilateral elements, then the physical coordinates and mesh displacements (if active) will be interpolated using quadratic basis functions, whereas other degrees of freedom, e.g., temperature or voltage, could use linear shape functions.

Documents containing results obtained through use of this software should cite

    @TECHREPORT{
      SAND2025-03448O,
      author = "Sierra Thermal Fluids Team",
      title = "SIERRA Multimechanics Module: Aria User Manual - Version 5.24",
      institution = "Sandia National Laboratories",
      year = "2025",
      type = "{SAND Report}",
      number = "2025-03448O",
      address = "Albuquerque, NM and Livermore, CA"
    }