The acoustics solvers in CAA++ range from analytic, algebraic methods, to full numerical field solvers. The simplest analytic methods are based on acoustic-analogy concepts, allowing users to quickly estimate near- or far-field spectra at a small number of probes, given a set of stationary statistics (RANS solutions). CAA++ also includes a range of signal-processing tools and methods to estimate total acoustic power output, in addition to providing a visualization of the local sound sources. More advanced methods in the CAA++ suite rely on numerical solutions to disturbance equations, that can account for bulk fluid motion, resonance, refraction & reflection from solid surfaces.
	A Hierarchical Approach to Noise Prediction A number of advanced computational aeroacoustics techniques have been assembled in the CAA++ suite, providing users with a range of methods to suit available computing resources. CAA++ contains simple analytic methods, that allow rapid inspection of noise source regions or the computation of spectra at user-defined virtual acoustic probes. CAA++ also contains numerical solvers that provide a great degree of generality. Each of the the CAA++ tools rely on a realizable set of statistics being provided as input. To achieve this, CAA++ integrates effortlessly with CFD++, with CFD++ creating the necessary acoustics data files, describing relevant mean field data, in addition to the statistics on the turbulent fluctuations. Analytic Methods Acoustics prediction methods required by industry are expected to handle a substantial range of Reynolds number and finite computing resources dictate that some form of mathematical modeling can be required in order to keep simulation costs within attainable bounds. CAA++ provides algorithms based on analytic wave-propagation methods, that can rapidly and efficiently compute acoustic spectra for a small number of user-defined probe locations. In addition, such analytic methods can be integrated (with certain assumptions on anisotropy and spherical acoustic-wave transmission) to produce an estimated measure of volumetric power-output that can be visualized to examine near-field sources of sound, or integrated to determine the final acoustic power output from a given configuration. An important motivation for the use of acoustic analogies and analytic (or numerical) wave-equation solvers is in the prediction of acoustics from low Mach number flows. At low Mach numbers, the differences between the spatial scales associated with the vortical disturbances in the fluid and the resulting acoustic waves can be considerable. For example, the Kolmogorov scale at sea-level conditions is approximately 2e-5m, whereas acoustic wavelengths audible to humans can be of the order of 1m or more. Variation in scale of particle wavelength and acoustic wavelength leads to large variation in grid requirements. Synthetic Turbulence   To avoid the difficulties associated with these disparate length-scale requirements, the CAA++ solvers utilize an advanced synthetic model of turbulence that provides a description of the unsteady flow at all relevant wavelengths, including those at sub-grid scales. To do this, CAA++ uses a reconstruction involving a modeled set of Fourier modes, generating a realistic set of disturbances that match a given set of statistics.    Non-Linear Acoustics Solver   Extensive use of modeling inevitably leads, at some point, to situations that deviate too far from the model calibration range to provide meaningful solutions. Consequently, the usefulness of simplified wave-equation solvers are typically limited to a restricted class of problem. The CAA++ Non-Linear Acoustics Solver (NLAS) allows for much greater generality, by numerically modeling both acoustic disturbances and some of the larger-scale fluctuations comprising the noise sources. The method is based on the solution of disturbance equations, which describe perturbations around a mean set of data, which is provided (along with relevant statistics) by CFD++. The CAA++ solvers, including NLAS, can be used with the same arbitrary geometries and meshes as CFD++. NLAS allows important large-scale generation effects to be captured directly on the mesh and provides a means of modeling reflection, refraction and blocking effects caused by the presence of complex surface geometries. NLAS offers a number of interesting capabilities. Calculations can be performed on separate acoustics meshes, which can require less near-wall resolution and a reduced far-field extent, due to specialized boundary-condition treatments. The benefits of this are that the acoustics solver can operate on more isotropic cells (particularly in the near-wall region, where a grid converged RANS solution is already available), resulting in a reduction in the overall number of mesh points from the relaxed near-wall requirements and a suitably truncated outer domain. Truncated outer boundaries in NLAS are assigned self-tuning absorbing layer boundary conditions, with far-field (and damping layer) data provided by the (a priori) RANS solution. This provides a good description of the outer boundaries and minimizes spurious wave reflections back into the simulation domain, even for boundaries located close to the source region of interest.   Absorbing layers (constant coefficient). Absorbing layers (self-tuned coeffient). Compared with direct numerical simulation (DNS), the reduced grid requirements of a traditional LES are rather minimal, particularly in the near-wall region.  Hybrid RANS/LES methods can achieve a reduction in mesh size by eliminating the mesh requirements in planes parallel to the wall (the normal-to-wall resolution is still required for the near-wall RANS modeling). NLAS further relaxes these meshing requirements, since a priori RANS statistics are always available, even on coarser regions of the NLAS mesh.   Required near-wall mesh resolutions with (from left to right) DNS, traditional LES, hybrid RANS/LES and non-linear acoustics solver (NLAS) based on disturbance equations.