Applications

Navier-Stokes-Simulation
Molecular-Dynamics
Adaptive Parallel Multigrid

Navier-Stokes Simulation

In this project we develop a sufficiently fast and accurate CFD code. NaSt3D\GP is a C++ implementation of a Chorin type projection method. For the spatial discretization finite differences on a non-uniform, rectangular mesh are employed. The temporal discretization bases a first order forward Euler scheme (see also: current work). Much emphasize is laid on the point that even complex problems, such as flows around complicated geometries, can be defined in a very clear and easy way, to rapidly obtain numerical results. Our approach rests on two concepts. First, there is a simple macro-language with a few but powerful and meaningful key-words to describe the flow configuration. This allows the user to

build complex geometries by union, intersection, subtraction of CSG (Constructive Solid Geometry) primitives using shape parameters independent on the discretization
describe the computational mesh in a simple way
define various parameters, e.g. Reynolds number, stopping value for iterative solver, upwind parameter

Poppelsdorf campus

To supplement the features of this macro language some special tools are available (see: tools).

The second concept is the clear and open structure of the code itself. This should allow for easy and save modifications of NaSt3D\GP for problems which are not yet covered, e.g. time-dependent inflow conditions.

NaSt3D\GP is fully parallelized, but can be compiled in a single processor version if no message passing library is installed in the users environment.

Molecular Dynamics

Attila Caglar

A major difficulty in MD-simulation methods is the complexity of the long range force evaluation in each time step. To cope with this problem, various multiscale type methods had been developed, i.e. treecodes, multipole approaches or multigrid techniques, which reduces the O(N^2) complexity of the naive approach to O(N log N) or even O(N).

A further reduction on execution time is possible by parallelization. Here, however - especially for adaptive tree-type methods - the implementation is quite difficult and cumbersome.

Our approach, which we have now implemented, is a variant of the adaptive Barnes-Hut/Multipole method (see also: J.K. Salmon & M.S. Warren, Int. J. Supercomp. App. , Vol.8.2). We use a hash-technique for dealing with the adaptivity of the method and parallelize with space-filling curves by assigning segments of the increasingly ordered hashtable-key list to each processor.

Altogether this results in an efficient long-range (Coulomb, van der Waals) force evaluation without potential cut-off and a simple incorporation of short-range forces.

NaCl
melting NaCl

crystaline Argon

Butane

Polyethylene

2D fracture

3D fracture

Adaptive Parallel Multigrid

Gerhard Zumbusch , Michael Griebel

We are interested in the solution of boundary value problems of partial differential equations. As a prototype we choose the Poisson equation. Two typical solutions on adapted grids, computed with a finite difference discretization looks like this:

2D grid

3D partition

We want to construct an efficient solver, which uses an optimal order solution algorithm (multigrid), a low number of unknowns (adaptivity), very little memory (hash storage) and runs on large parallel computers. Especially the grid adaptivity poses some difficulties for the parallel implementation.