Immersed Boundary Methods within a PDE Toolbox on Distributed Memory Systems
Janos Benk · mediaTUM – the media and publications repository of the Technical University Munich (Technical University Munich) · 2012
Advanced simulation of complex physical systems governed by partial differential equations (PDE) poses significant computational challenges that require a collection of sophisticated numerical methods. One of the main challenges is the representation of complex boundaries and domains together with the respective boundary conditions (BC). In the classical way, this challenge is tackled by a costly mesh generation process, that becomes a significant computational bottleneck especially on distributed memory systems. The time to solution is a crucial factor for modern PDE software development. Hence, combining new numerical methods into a user-friendly PDE toolbox that also allows parallel simulations is a significant algorithmic and software design challenge. This thesis describes contributions to the development of various complex boundary representations in the form the Immersed Boundary (IB) methods within the frame of the PDE toolbox Sundance, a package within the Trilinos project. The IB methods use a memory- and cache-efficient structured mesh in combination with special methods to impose the BCs on complex boundaries. We extended Sundance with parallel structured mesh implementation, while general cut-cell and boundary integral methods were developed in the frame of Sundance, allowing the implementation and parallel computation of various IB methods in this toolbox environment. The one particular IB method in our focus is Nitsche's method for flow simulation that allows moving boundaries even for a fixed mesh approach, and significantly simplifies the obstacle representation in the flow field. To demonstrate the capabilities of our IB approach and Sundance implementation we computed various benchmark scenarios in 2D and 3D settings. The presented results of the strong scaling study show the scalability on distributed memory systems. This work, thus, is an important step towards IB methods in a PDE toolbox context, capable of distributed memory simulation.