A subcell remapping method on staggered polygonal grids for arbitrary-Lagrangian–Eulerian methods

Abstract

We describe a new remapping algorithm for use in arbitrary Lagrangian–Eulerian (ALE) simulations. The new features of this remapper are designed to complement a staggered-mesh Lagrangian phase in which the cells may be general polygons (in two dimensions), and which uses subcell discretizations to control unphysical mesh distortion and hourglassing. Our new remapping algorithm consists of three stages. A gathering stage, in which we interpolate momentum, internal energy, and kinetic energy to the subcells in a conservative way. A subcell remapping stage, in which we conservatively remap mass, momentum, internal, and kinetic energy from the subcells of the Lagrangian mesh to the subcells of the new rezoned mesh. A scattering stage, in which we conservatively recover the primary variables: subcell density, nodal velocity, and cell-centered specific internal energy on the new rezoned mesh. We prove that our new remapping algorithm is conservative, reversible, and satisfies the DeBar consistency condition. We also demonstrate computationally that our new remapping method is robust and accurate for a series of test problems in one and two dimensions.