Application of PML Absorbing Boundary Conditions to the Benchmark Problems of Computational Aeroacoustics

Accurate numerical non-reflecting boundary conditions are important in all the proposed benchmark problems of the Second Workshop. Recently, a new absorbing boundary condition has been developed using Perfectly Matched Layer (PML) equations for the Euler equations. In this approach, a region with a width of a few grid points is introduced adjacent to the non-reflecting boundaries. In the added region, Perfectly Matched Layer equations are constructed and applied so that the out-going waves are absorbed inside the layer with little reflection to the interior domain. It will be demonstrated in the present paper that the proposed absorbing boundary condition is quite general and versatile, applicable to radiation boundaries as well as inflow and outflow boundaries. It is also easy to implement. The emphasis of the paper will be on the application of the PML absorbing boundary condition to problems in Categories 1, 2, and 3. In Category 1, solutions of problems 1 and 2 are presented. Both problems are solved using a multi-domain polar grid system. Perfectly Matched Layer equations for a circular boundary are constructed and their effectiveness assessed. In Category 2, solutions of problem 2 are presented. Here, in addition to the radiation boundary conditions at the far field in the axisymmetric coordinate system, the inflow boundary condition at the duct inlet is also dealt with using the proposed Perfectly Match Layer equations. At the inlet, a PML domain is introduced in which the incident duct mode is simulated while the waves reflected from the open end of the duct are absorbed at the same time. In Category 3, solutions of all three problems are presented. Again, the PML absorbing boundary condition is used at the inflow boundary so that the incoming vorticity wave is simulated while the outgoing acoustic waves are absorbed with very little numerical reflection. All the problems are solved using central difference schemes for spatial discretizations and the optimized Low-Dissipation and Low-Dispersion Runge-Kutta scheme for the time integration. Issues of numerical accuracy and efficiency are also addressed.