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Center for Nonlinear Studies |
The resonator-type problems can be considered as typical problems in nonlinear aeroacoustics. One of the actual examples of such problems is simulation of noise suppression in resonant liners. An effective design of noise absorbing panels needs a deeper understanding of determining physical mechanisms, from one hand side, and a convenient testing simulator for their quick optimization, from another. A wide range of accessible geometrical parameters, possible amplitude and frequency characteristics of incoming acoustic signal complicate the experimental study, and make the numerical simulation an attractive testing tool. At simulating the resonator-type problems numerically, specifics are that in the case of rather high acoustic power of incoming signal, the computational domain under study covers both "linear" and "nonlinear" regions. In the "linear" region, the acoustic wave propagation is a determining physical process which needs high accuracy numerical algorithms for its proper resolution. In "nonlinear" regions the corresponding numerical techniques have to be adapted to the possible solution discontinuities. So the algorithms of nonlinear aeroacoustics have to combine the better properties of linear CAA and nonlinear CFD in some adaptive way since there is no definite space bound between "linear" and "nonlinear" operating zones. A difficulty in constructing the schemes of this kind becomes especially serious when applied to arbitrary unstructured meshes. At the same time, the matters are improved by the sufficient smoothness of the solutions under consideration including only weak jumps. I present a finite volume algorithm for solving nonlinear aeroacoustics problems on unstructured meshes. It is based on the high accuracy vertex-centered multi-parameter scheme. It is built in a way of superconvergence meaning that it achieves its up to the 6th theoretical order of accuracy on the Cartesian meshes. Different formulations of resonator-type problems are considered. The first simulates a resonator chamber of rectangular and curvilinear shapes, its goal is to find a resonant frequency. This formulation serves also for the verification of numerical techniques used by comparing the results with the a priori known theoretical or experimental data on the resonator properties. The second group of problems presents numerical experiments on sound suppression in resonance-type liners and corresponds to the conditions of physical experiment in waveguides ended by a resonator box which is separated by a perforated screen. And the third formulation can be considered as a model for engineering experiment. It investigates the acoustic energy losses of the flow in the channel with a perforated wall.