Tangle-free Finite Element Mesh Motion for Ablation Problems

Abstract

JSC Engineering, Technology, and Science (JETS): Jacobs Technology and HX5, LLC Mesh motion is the process by which a computational domain is updated in time to reflect physical changes in the material the domain represents. Such a technique is needed in the study of the thermal response of ablative materials, which erode when strong heating is applied to the boundary. Traditionally, the thermal solver is coupled with a linear elastic or biharmonic system whose sole purpose is to update mesh node locations in response to altering boundary heating. Simple mesh motion algorithms rely on boundary surface normals. In such schemes, evolution in time will eventually cause the mesh to intersect and "tangle" with itself, causing failure. Furthermore, such schemes are greatly limited in the problems geometries on which they will be successful. This paper presents a comprehensive and sophisticated scheme that tailors the directions of motion based on context. By choosing directions for each node smartly, the inevitable tangle can be completely avoided and mesh motion on complex geometries can be modeled accurately.

3D mesh displacement strategy to simulate the thermal degradation of materials under atmospheric reentry conditions

“…4). To prevent this pathological behaviour and to correctly displace structured and unstructured meshes, boundary conditions are generally defined as stationary, sliding or ablating as done by Droba [14]. Then, a treatment is applied to each vertex depending on the type of boundary surface around it.…”

“…Indeed, when a corner vertex is smoothed, the intersection between the 3 planes around it is no longer defined. The strategy described by Droba [14] allows to deform complex geometries in 2D. However, the 3D strategy was not verified with test cases and the formulation seems inadequate for shape changes.…”

“…Then, the optimal displacement distance is chosen to remove the exact ablated mass in the least square sense. The main advantage of this method compared to Droba [14] method is that singularities of the geometry are managed without a preliminary classification. However, the wavefrontal motion for the surface displacement never preserves the object shape.…”

“…At first, the Sinusoidal Slider test case of Droba [14] illustrated in Fig. 20 is used to validate the vertex displacement on concave and convex surfaces.…”

Overview of the CHarring Ablator Response (CHAR) Code

“…Current effort is focused on the implementation of the boundary conditions developed by Droba. 17 Additionally, the development team intends to explore other PDE based methods for mesh motion and smoothing such as solving the bi-harmonic equation. Finally, other non-PDE based methods, such as the one presented by Luke et al, 41 will also be investigated for speed and mesh quality under large deformations.…”