The aim of the AcousticSolver is to predict acoustic wave propagation. Through the application of a splitting technique, the flow-induced acoustic field is totally decoupled from the underlying hydrodynamic field.
The Linearized Euler Equations (LEE) are obtained by linearizing the Euler Equations about a mean flow state . Hence, they describe the evolution of perturbations around this state. In conservative form, the LEE are given as:
| (6.1) |
with
(6.2) (6.3) (6.4) |
The acoustic perturbation equations (APE-1/APE-4) proposed by Ewert and Schroeder [12] assure stable aeroacoustic simulations. These equations are similar to the LEE, but account for acoustic perturbations exclusively. The AcousticSolver implements the APE-1/4 type operator:
where (u,c^{2},ρ) represents the base flow and (u^{a},p^{a}) the acoustic perturbations. Similar to the LEE, the acoustic source terms _{c} and _{m} are by default zero and must be specified e.g. by an appropriate forcing. This way, e.g. the APE-1, APE-4 [12] or revised APE equations [15] can be obtained. Expressed as hyperbolic conservation law, the APE-1/4 operator reads:
| (6.6) |
with
(6.7) (6.8) |