SWAGE: A 3D Arbitrary-Order Element Mesh Library to Support Diverse Numerical Methods

Abstract This paper presents the details on a new open-source swift arbitrary Lagrangian Eulerian (SWAGE) software library that supports diverse numerical methods on unstructured, arbitrarily moving curvilinear meshes — from stationary (Eulerian) to moving at the fluid velocity (Lagrangian), and anywhere in between (arbitrary Eulerian Lagrangian). Each element of the unstructured mesh in the physical coordinate system is represented by a spatial map from a single reference element. Foundational numerical methods are provided in the reference element that are key to solving diverse types of physical equations and calculating geometric quantities. A large set of index spaces in the physical coordinate space and the reference coordinate space are provided in SWAGE and the companion reference element type library respectively. Mesh connectivity data structures are provided to access various index spaces or a neighboring index on the physical mesh or within the reference element. The SWAGE mesh library supports continuous finite element, finite volume, and discontinuous Galerkin (DG) methods using arbitrary-order 3D curvilinear elements. The SWAGE library fills an existing technology gap by supporting arbitrary-order 3D Lagrangian DG hydrodynamic methods, along with many other numerical methods and solvers. The Lagrangian DG hydrodynamic method requires unique index spaces and very intricate mesh connectivity structures not currently available in other open-source libraries. The details of the SWAGE library are presented in this paper along with examples and results.