### Mathematical Research at FSU

#### Aeroacoustics

Dr. Tam and his collaborators are pioneers in the use of large-scale numerical simulation to solve aircraft and other transportation noise problems; a research area known as computational aeroacoustics (CAA). Numerical simulation not only provides quantitative prediction of a problem but the full space-time data of the computation offers a researcher the opportunity to seek the underlying physics and noise generation mechanisms of the phenomenon. Acoustic waves are non-dispersive and non-dissipative. Thus the use of a non-dispersive and non-dissipative CAA algorithm such as the Dispersion-Relation-Preserving (DRP) scheme is extremely desirable. Aeroacoustics problems, intrinsically, have multi-scales characteristics. For instance, it is known that one of the dominant components of jet noise is generated by the fine scale turbulence of the jet flow. To resolve the small-scale turbulence, a fine computational grid is required. However, just outside the jet flow in the acoustic field, the acoustic wavelength could be several jet diameters long. Here a coarse grid with 7-mesh points per wavelength would provide sufficient spatial resolution. For CAA problems of this kind, the use of the multi-size-mesh multi-time-step DRP scheme would be most efficient. At takeoff, an aircraft requires maximum power. This means that propulsive noise, such as jet noise, fan noise, combustion noise, would be dominant. At landing, the power is reduced. Now, noise from turbulent flow over the airframe, e.g. wings, slats, flaps and landing gears become just as important. This noise component is referred to as airframe noise. In Dr. Tam's group, application of CAA to jet noise of high-performance aircraft at afterburner, fan noise radiation, physics of acoustic liners, indirect combustion noise is a part of current research activities.