An Algorithm for Mesh Refinement and Un-Refinement in Fast Transient Dynamics

Abstract

A procedure to locally refine and un-refine an unstructured computational grid of four-node quadrilaterals (in 2D) or of eight-node hexahedra (in 3D) is presented. The chosen refinement strategy generates only elements of the same type as their parents, but also produces so-called hanging nodes along non-conforming element-to-element interfaces. Continuity of the solution across such interfaces is enforced strongly by Lagrange multipliers. The element split and un-split algorithm is entirely integer-based. It relies only upon element connectivity and makes no use of nodal coordinates or other real-number quantities. The chosen data structure and the continuous tracking of the nature of each node facilitate the treatment of natural and essential boundary conditions in adaptivity. A generalization of the concept of neighbor elements allows transport calculations in adaptive fluid calculations. The proposed procedure is tested in structure and fluid wave propagation problems in explicit transient dynamics.

On the dynamic response of blast-loaded steel plates with and without pre-formed holes

“…When a monitored parameter, typically the damage D , reaches a chosen value min D , the shells are refined by splitting each element into four smaller elements using the technique of Ref. [19]. The mesh refinement strategy is shown in Figure 9 for a quadrilateral.…”

“…[4], resulting in complete failure of the plates. Recent advancements including adaptive mesh refinement in EPX [19] are used in combination with element erosion to predict the crack propagation observed in the experiments. Material tests were also performed to determine the material behaviour at large plastic strains and to identify the parameter in an energy-based failure criterion.…”

Propeller blade debris kinematics

“…This is precisely the scope of adaptivity: to refine the fluid mesh only where it is needed, in this case close to the structure (FSI-driven adaptivity). The general strategy adopted in EPX to adaptively refine and un-refine the computational mesh is described in [15]. FSI-driven adaptivity is best used in conjunction with an embedded FSI algorithm such as FLSW, see [16].…”

Goal-oriented space-time adaptivity for transient dynamics using a modal description of the adjoint solution

“…The space meshes P n are built considering a hierarchical tree-based mesh refinement strategy [6,8,31]. In this framework, the computational meshes are obtained recursively splitting the elements of an initial background mesh denoted as P bg as shown in figure 1.…”