Mesh Adaptivity

From AMCGMedia

Introduction

Critical to any state-of-the-art unstructured mesh finite element model is the ability to dynamically resolve developing solution features (e.g. shock waves, fronts, eddies) whose positions are not necessarily known a priori to the simulation. Mesh adaptivity methods allow the mesh to be locally optimised to resolve such flows in response to an error metric which is generally derived from either the solution, or the partial differential equations describing the system dynamics and modelling goals.

AMCG has developed an efficient parallel adaptive unstructured mesh method suitable for steady state and transient finite element modelling. The key features of the mesh adaptivity method are: it is an optimisation based method; the optimisation seeks to minimise an objective function written in terms of a Hessian based metric tensor; optimisations are carried out iteratively through trials of local changes in the mesh connectivity (h-method) and node movement (r-method). The Gauss-Seidel iterative nature of the algorithm complicates the optimisation of the elements that are shared between sub-domains. The approach adopted by AMCG locks these shared regions so that the serial algorithm can be applied to each sub-domain independently. Careful tuning of the subsequent graph partitioning ensures that substandard elements that were previously located are later made internal to a sub-domain so that they are free to be optimised when the serial adaptivity algorithm is reapplied. The additional cost of the required graph repartitioning and data remapping can be effectively hidden by the requirements and cost of dynamic load-balancing.

A simple example of anisotropic adaptivity

Three fields placed across a cube, adapting to the error measure from all three fields. The cubes to the left show initial mesh, first adapt, and second adapt. More info...

Flow Past a Heated Cylinder

Reynolds number of 2000. Includes animations of the flow, showing both mesh and temperature field. The image to the right shows a snapshot of the mesh during the simulation.

3D Flow Past a Heated Sphere

Reynolds number of 400. Includes animations of the flow, showing mesh and temperature. The picture to the left shows a snapshot of the mesh during the simulation, with a chunk of the domain removed to enable a view of some of the internal elements near the sphere and the flow wake.