Funded by



Simple example of an adaptively refined tree-structured grid in two dimensions (right: corresponding tree-structure of the grid cells on all refinement levels; red: morton ordering of grid cell on locally finest grid level).

Adaptively refined computational grids are a very efficient method to extend the computable domain size and time span. They keep the number of grid points and, therewith, the number of operations at a feasible level. If the scenario changes within the simulated time span, the local resolution of the grid has to be adapted. Tree-structured adaptive grids have the advantage over other grid types that they come with minimal storage requirements due to the clearly defined refinement structure... At the same time, they can be efficiently partitioned with a good load balancing. In spite of the structuredness, these grids offer arbitrarily local and dynamic refinement options. The difficulty in using them for existing simulation codes is, on the other hand, also due to the special structure and the wish to fully exploit its advantages. In the ideal case, the algorithm of the simulation program follows the tree-structure. However, this in general requires deep and inaccetably time consuming changes of the entire code. As a consequence, many applications treat tree-structured grids as unstructured grids, thus storing all relations between grid vertices, edges, faces, and elements and loosing almost all advantages of the structuredness. As for todays and even more for tomorrows computer architectures low memory requirements, efficient memory access, and a good parallelizability are decisive for the overall software efficiency, an urgent need arises for the development of concepts translating tree-structured grids into efficient data structures that still allow the users to process grid data based on simple iterators, i.e., loops over grid components. To optimally exploit cach hierarchies, the underlying data structures should in addition yield a high spatial and local locality of data access and preserve this property also in case of dynamically adaptive grid refinement. The task of this project is the development and implementation of such a concept as well as the application for problems from the collaborative research centre that urgently need an extension of the comutable domain size and time span to achieve sufficiently accurate simulation results.

E.g., in projects B5 (laser ablation) and C5 (macromelocular transport in nanoscale pores) continuum mechacanical background simulations (fluid flow, electro kinetics, temperature in a two-temperature model) are simulated on currently regularly refned Cartesian computational grids and combined with molecular dynamics simulations. In both cases, a further extension of the simulation domain in space and time is required to reduce artificial influences of physically incorrect boundary or initial conditions and to achieve representative results. Adaptive grids can be used efficiently in these projects as both for the transport of DNA through a pore (project C5) and for laser ablation processes (project B5), only small parts of the domain where the actual interaction between particles or with domain boundaries happens have to be treated with high accuracy. With this approach, e.g., the spatial scale in C5 shall be extended from nanometers to micrometers. In cooperation with the respective project teams, suitable discretization approaches for the underlying models have to be found in addition to the grid concept described above. Additionally, domain decomposition and load balancing methods have to be defined and simulation results have to be validated by comparison with regular grid results.

In project A6, a coupling of a Smoothed Particle Hydrodynamics solver for the morphology formation with a Lattice Boltzmann solver for the efficient simulation of an adjacent free flow domain shall be implemented. This represents a further ideal application area for the adaptive LBM code developed in D8. Further connections exist with the projects A8 (agglomeration of particles in turbulent flows) and B8 (laserdriven ablative expansion processes), where the combination of kontinuum mechanics with particle methods is also used.

In B2 (intenal boundary layers in copper alloys), an enhancement of the existing model for molecular metal lattice structures is to be developed that includes the possibility of substantial deviations of molecules' positions and their structural interactions from the regular lattice structure. Also in this case, adaptive grid structures for three representation of the particle positions might be used.

Results simulated on adaptively refined grids require a subsequent modification of visualization methods as data points are not regularly distributed in sapace any more, but have to be localized according to their position in the grid tree. The work packages required to achieve these changes are going to be tackled in cooperation with D3 and D5.

Beyond the collaborative research center, the developed methods and software packages from D8 offer new possibilities to enhance also other simulation applications from regular to adaptive grid structures in a relatively easy and minimally invasive way. Currently, numerous implementations of interfaces for unstructured grids are available that, however, destroy all advantages of the particular grid type. An easy to use interface actually exploiting the advantages induced by the structure, would be very valuable for a large variety of applications.