Browsing by Author "Utzmann, Jens"

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A domain decomposition method for the efficient direct simulation of aeroacoustic problems
(2008) Utzmann, Jens; Munz, Claus-Dieter (Prof. Dr.)
A novel domain decomposition approach is developed in this thesis, which significantly accelerates the direct simulation of aeroacoustic problems. All relevant scales must be resolved with high accuracy, from the small, noise generating flow features (e.g., vortices) to the sound with small pressure amplitudes and large wavelengths. Furthermore, the acoustic waves must be propagated over great distances and without dissipation and dispersion errors. In order to keep the computational effort within reasonable and feasible limits, the calculation domain is divided into subregions with respect to the local physical requirements. In these domains, the numerical method which is most suitable and optimized for the considered subproblem is employed. The proposed method differs from established approaches, e.g. the grid coupling is not limited to Chimera techniques but presents a consistent way for the space-time coupling of high order methods. Various domain decomposition options are examined and implemented in a common code framework. In the subdomains, the Navier-Stokes, Euler and linearized Euler equations are solved, for which methods from the discontinuous Galerkin (DG), finite volume (FV) and finite difference (FD) class are available with their respective special properties. For example, DG methods are very suitable for highly accurate solutions on unstructured grids due to their locality, while FD methods are very efficient on Cartesian grids for the simulation of linear wave propagation. In turn, FV methods are very robust in the presence of strong gradients, e.g. shocks. All implemented methods have in common, that they are explicit one-step time integration schemes and thus are especially applicable for unsteady calculations. Furthermore, their order of accuracy in space and time may be chosen arbitrarily. A newly developed numerical solver, the STE-FV method on Cartesian grids, closes the gaps in the repertoire of numerical schemes in the coupling framework. It forms a fast high order method that features great robustness also at nonlinearities by employing a WENO algorithm. For validation purposes, convergence studies and benchmark tests, e.g. the popular double Mach reflection in 2D and an explosion in 3D, are performed for the STE-FV method with orders in space and time up to six and beyond. The coupling of different grids is based on high order interpolations and the data exchange over the ghost elements of the calculation domains. The Gauss integration points in the cells are used here in order to find a source domain for the interpolation and for providing high order boundary conditions afterwards. The grids are not required to be matching or overlapping. Furthermore, arbitrary constellations of structured and unstructured grids are possible. The optimal time steps, which can be different of each other, are allowed in the subregions. This is made possible by employing the Cauchy-Kovalevskaja procedure, which delivers a Taylor series that provides boundary information for the intermediate points of time for domains with a smaller time step. The implementation structure inside the code framework is largely modular. The fluid and acoustics solvers can be used as stand-alone codes, and also new ones can be easily added. Furthermore, external programs, which may run on separate computer systems, can be linked to the framework. The distribution to different system architectures is also possible for the internal solvers. Hence, the respective properties of the numerical methods regarding vectorization and parallelization can be exploited in an optimal way. It is shown on the basis of convergence studies for different constellations of grids, equations and methods, that the domain decomposition approach is capable of maintaining high order of accuracy globally. An examination regarding high-frequency perturbations reveals a natural filtering process if perturbations cannot be resolved on a coarse mesh anymore. Hence, a spatial filtering operator is not a necessity. Another study shows, that the magnitude of reflections occurring at the domain boundaries are in good accordance with theoretical estimations. Besides the change from nonlinear to linear equations, also the jump in resolution matters in this context. However, the reflections are negligible in general. The accuracy and efficiency of the proposed domain decomposition method is illustrated for benchmark examples like the acoustic scattering at a sphere or at multiple cylinders and for the Von Karman vortex street. Here, especially the method's potential for efficient far field calculations becomes clear, but also the advantages in the presence of complex geometries are emphasized. Finally, the simulation of a nozzle flow with a supersonic free jet and the associated noise underlines the practical applicability of the domain decomposition approach.