Modern applications in Computational Science and Engineering such as
fluid-structure interactions demand for efficient algorithms to simulate the
corresponding physical phenomena.
Many of those applications rely on an efficient flow solver for the
Navier-Stokes equations as the underlying partial differential equations (PDE).
Designing a stand-alone tool tailored to the concrete type of problem
or discretisation scheme enables full access to all features of the code or
algorithm but comprises the drawback
of a lack of flexibility, due to the dependency of a lot of features such
as efficient and adaptive mesh generation, dynamic mesh adaption, support of
complex geometries, parallelisation, support of different algebraic solvers and
time integration schemes, or post-processing devices
on the concrete realisation.
Hence, recent solvers rely on frameworks for PDE that try to overcome
these drawbacks by collecting a lot of the common tasks in a centralised and
automated way.
This thesis presents the design, implementation and validation of a modular
solver for incompressible flow problems in the PDE framework Peano.
Peano uses adaptive Cartesian grids in arbitrary dimensions and combines
space-filling curves and a stack data structure concept to support challenging
features such as dynamically
changing grids efficiently.
Two- and three-dimensional spatial discretisation of the underlying equations is
realised via low-order finite elements (FEM) and higher-order integrated
differential operators (IDO), while different explicit and implicit time
integration methods of various orders are supported.
Several benchmark simulations demonstrate the successful combination of, on the
one hand, the various features necessary for a modern flow solver, and, on the
other hand, keeping good performance results such as high cache-hit rates and low
memory demands.
Thus, Peano represents a powerful environment for efficient CFD simulations.
The scope of its concept is directly extendable to many other fields of
numerical simulation of PDE.
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