| A central focus in this research project is the accurate and efficient modeling and simulation of flows of complex fluids and of complex physical phenomena in simpler(Newtonian) fluids. Problem-areas involving complex fluids are umerousand range,e.g.,from biology,medicalphysics,geo-physicaland environmental lows to applicationsinprocess-engineering,and may involveheat- and asst ransfer,complexgeometries,multi-phase flows,chemical reactionsand non- Newtonian stress relations. Likewise, complex phenomena in simpler fluids involve boundary layers and their separation,the effects of rotation and(fractal) forcing on(in)homogeneous structures int urbulent flows,t hebehaviorof alargenumberofinteractingparticlesinaturbulent(riser)flowand theoccurrence of shocks in compressible flows at high Mach numbers. The dynamics of these fluids is governed by systems of nonlinear partial differential equations, such as the Navier-Stokesequations,possibly coupled to alargenumberof ordinary and/orpartial differential equations which could, e.g., describe the motion of embedded particles or bubbles such as may arise in multi-phase or granular flows or represent the interaction between the flow and mechanical structures, such as elastic walls. In order to address the simulation of this kind of problems, in general three different aspects must be considered: the modeling of the flows, the numerical methods used to perform calculations with these models, and the implementation of these methods on suitable computers. We turn to this next. Modeling of the flow of complex fluids. In order to arrive at an accurate description of the dynamics of complex fluids one may distinguish between the physical modeling and the amount of detail with which this physical modelis(requiredtobe) resolved. In the physical modeling detailed phenomeno logical 1 picture of the constituents of the fluid is translated into a dynamical system, which may, e.g., take the form of non-Newtonian constitutive equations or leads to directly accounting for the presence of interacting particles or bubbles as part of the fluid, such as may occur in dispersions or emulsions. Of equal importance are external effects which may considerably modulate the developing turbulent flow. Examples of such effect sarerotationand stratification,but also the interaction with complexobstructing objects such as foams, or with intense, localized combustion may seriously alter the turbulent flow. Once the detailed physical modeling is available, one may decide to resolve all spatial and temporal features of the dynamical system and aim at a grid-independent numerical solution. This corresponds to adirect numerical simulation(DNS).However,in many instancesitis notfeasible or not required to resolve all flow features and a coarser description may suffice. This corresponds to large-eddy simulation (LES). In LESan external length-scale is introduced into the description which is identified with the width of the spatial low-pass filter with which the Navier-Stokes equations are filtered. Only features in the flow larger than are explicitly resolved in the simulation while the dynamical effects of the 'sub- ' scales need to be parameterized by a suitable subgrid model. Thus, in LES the computational effort can be strongly reduced compared to DNS while with proper selection of sufficient flow detail may be retained to provide accuratepredictionsof various flowproperties. Thestudy of thedynamicsof complex fluidsisanewpacingitemfordirect andlarge-eddy simulation. Inparticular,thestudyof reactingflowsandflowscontainingparticlesandbubblesisofgreatimportance, boththeoretically aswell asinrelationtoanumberof applicationareas.A centralprobleminthiscontext is the combination of a spatially smoothed flow description and strongly localized flow-phenomena such as reaction-fronts or discrete particles moving along with a flow while simultaneously influencing this flow. By adopting new 'approximate inverse modeling' and 'regularization modeling' in the context of large-eddy simulation and global level-set dynamics a suitable combination of retained flow detail and computational effortmay beachieved,which may allowsufficiently accuratepredictionsforrealistic flow conditions and geometries. The development and investigation of these complex-fluid simulations is a main research item in this project. Numerical methods and implementation. In order to be able to perform direct numerical simulations in three spatial dimensions, next to the formal order of accuracy of the method, the efficiency of the numerical algorithms is a critical issue. Also, large-eddy simulations in more complex geometries and more complicated flow-fields can not be performed without an efficient algorithm. Moreover, systematic parameter-studies of certain flow-phenomena form a third reason which emphasizes the efficiency of the numerical algorithm. The numericalmethod starts from the conservative form of the governing equations,e.g.,the(filtered) Navier-Stokes equations. The conservation property is retained in the discrete equations by using, e.g., (pseudo-)spectralmethods,(discontinuousGalerkin) finite element formulations or general finite volume methods of different complexity and different formal order of accuracy. The unsteadiness of the solution in all problems considered in this project, requires an integration in time. We use explicit Runge-Kutta methods or second-order accurate implicit methods for this purpose. The system of equations resulting fromtheimplicittime-discretizationcanbesolvedby mean sofpseudo-time-stepping whichisaccelerated by a nonlinear multi-grid technique or using a quasi-Newton method with polynomial pre-conditioning. The basic finite volume method is embedded in a block-structured flow solver, in which the flow-domain is decomposed into several sub-domains. On a parallel platform, the decomposition can be used to obtain an efficient parallelization. Likewise, good parallel performance has been achieved with a proper implementation of ourpseudo-spectral method. Thecomputer-platforms whichseemtobesuitableforthiskind ofproblemsarevectorsupercomputers and massively parallel platforms of whichTERAS/ASTER is aprominent example. OnTERAS/ASTER, good efficiency of the numerical methods was achieved by developing a near optimal implementation for this platform over the past years. By relying on MPI for the parallel processing, some of the desired portability of the resulting codes can be achieved. Also, significant enhancement of the computational capabilities was obtained by parallelizing the code using OpenMP. |
