| An essential tool in studying flow problems is computational fluid dynamics (CFD). CFD is a collective term for a large number of numerical techniques, often each with its own area of application. The last decades have shown a growing knowledge of the fundamental concepts of CFD, and the efficiency of numerical algorithms has progressed at a considerable pace. It is foreseen that this growth will continue for some time. Although much emphasis is on turbulent flows at high Reynolds number and multi-phase or reacting flows (which are posing the more challenging problems from a physical point of view), insights in simpler problems may be equally useful and often even essential for constructing stable and efficient methods, to be used in more general contexts. Of the latter kind one should mention basic progress in iterative methods and in discretisation approaches. Iterative developments have shown widespread use of multigrid methods and special fast solvers for large linear systems. Combination with implicit time-integration can deal with the issue of stiffness in e.g. reacting flow. Discretisation methods are challenged by complex geometries and moving boundaries, and by large ranges of length- and time scales. Within the JMBC both Cartesian and unstructured (adaptive) grid approaches are being pursued to deal with the geometric and topological challenges. The (structured) Cartesian grid approach is combined with local grid refinement based on defect correction. The scale resolution problem is tackled e.g. by symmetry-preserving finite-volume methods (with a benign behaviour on underresolved flow features) and by space-time discontinuous finite-element methods (offering flexible spatial and temporal grid adaptation). Also unified algorithms for low-Mach number flow are under development. Further, following a different discretisation philosophy, Lattice-Boltzmann methods are being studied, which possess potential advantages in multi-phase flow simulation. Another important tool in enabling the computations to be performed in a 'reasonably limited' time is parallellisation. Besides a more straightforward use of multiprocessors where the parallelism is taken care of by the compiler, a variety of domain decomposition techniques is in development. In particular within a context where different flow modelling is used in the individual subdomains, research will open up interesting applications, e.g. in turbulent flow simulation where a mixture of RaNS, LES and/or DNS modelling can be envisaged. |
