The PDE Framework Peano: An Environment for Efficient Flow Simulations

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 PDE or discretisation scheme enables maximal 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 adaptation, 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. Twoand three-dimensional spatial discretisation of the underlying equations is realised via low-order finite elements (FEM) and higher-order interpolated 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.