Physical simulations often require the consideration of many phenomena
and scales. For example in aeroacoustic problems, both, the flow generating
the noise and the sound wave propagation needs to be considered. This work
investigates numerical approaches to such problems on large distributed and
parallel computing systems. The coupling framework KOP is parallelized
as far as possible and to overcome fundamental scalability limits a new
framework APES is developed. Both implementations utilize high-order
discretizations, as these allow for accurate simulations with less degrees of
freedoms than lower order methods. This property of high-order methods
is an important feature for modern supercomputing systems, as memory
to represent degrees of freedom in a simulation is a scarce resource. The
presented methods enable the transient simulation of multi-scale setups but
detailed resolutions still require large amounts of computational resources.
A focus is put on the efficient utilization of modern computing systems
to address this need. Besides the scalability of the implementations, the
importance of single core optimization and vectorization is illustrated.
KOP uses discrete points to realize the coupling and allows for the interaction
between domains with differing discretizations and solved equation
systems. Arbitrary mesh configurations are supported and both, structured
and unstructured mesh solvers are available in the framework. In both framworks
explicit time integration methods are deployed to resolve the time
dependent simulations. The coupling allows for a varying time step width
over the participating domains by a sub-cycling method. Various conservation
laws can be solved by the presented frameworks ranging from Maxwell’s
equations and linearized Euler equations to full compressible Navier-Stokes
equations. A fully distributed coupling approach is developed that allows
for coupling of those in a large-scale simulation to solve, for example, aeroacoustic problems.
APES enables high-order discretizations in the spectral regime. It involves
a fully scalable toolchain for mesh-based simulations featuring a mesh
generation and a post-processing tool to support the solvers. The common
foundation of these tools is an Octree representation for the mesh, and
this work specifically covers the generation of high-order geometry approximations in the developed mesh generator Seeder. This robust mechanism works for arbitrarily complex surfaces and offers a practical way to tackle
engineering tasks with spectral element discretizations.