We will report on our experiences implementing PDE solvers on Peta-Scale computers, such as the 290 000 core IBM Blue Gene system in the Jülich Supercomputing Center. The talk will have two parts, the first one reporting on our Hierarchical Hybrid Grid  method, a prototype Finite Element Multigrid Solver scaling up to a trillion (10^12)  degrees of freedom on a tetrahedral mesh by using a carefully designed matrix-free implementation.  The second part of the talk will present our work on simulating complex flow phenomena using the Lattice-Boltzmann algorithm. Our software includes parallel algorithms for treating free surfaces with the goal of simulating fully resolved bubbly flows and foams. Additionally, we will report on a parallel fluid-structure-interaction technique with many moving rigid objects. This work is directed towards the modeling of particulate flows that we can represent using fully resolved geometric models of each individual particle embedded in the flow. The talk will end with some remarks on the challenges that algorithm developers will be facing on the path to exascale in the coming decade.