Journal of Computational Acoustics

Due to their inherent dissipation and stability, the MacCormack scheme and its variants have been widely used in the computation of unsteady flow and acoustic problems. However, these schemes require many points per wavelength in order to propagate waves with a reasonable amount of accuracy. Recently, much progress has been made in improving the wave propagation qualities of MacCormack-type schemes. In this work, the linear wave propagation characteristics of MacCormack-type schemes are compared using several of the CAA Benchmark Problems.

While large-scale simulation of jet noise is the most thorough technique currently available for jet noise prediction, three-dimensional direct computation of both the near and far field requires prohibitive computational capability. In this work we propose to limit large-scale simulation to the near field to provide the pressure distribution over a cylindrical surface surrounding the jet. A surface-integral formulation is presented herein in which the calculated pressure on the cylindrical surface is used to obtain the far-field sound, without the need for the normal derivative of the pressure. The results are compared to that of direct large-scale simulation and to the zonal approach in which linearized Euler equations are used as an extension tool.

A method is presented for designing a one-step, explicit finite difference scheme for solving the inviscid Burgers equation based on an a priori specification of dissipation and phase accuracy requirements. Frequency accurate temporal and spatial approximations with undetermined coefficients are used, together with a set of constraints that ensure that the approximations converge as the spatial and temporal grid sizes approach zero and satisfy the Lax Equivalence Theorem. A practical design of the difference scheme using a heuristic zero placement method, combined with a stability requirement, results in a linear matrix problem which is solved to obtain the undetermined coefficients. The partial differential equation itself provides the relationship between the temporal and spatial frequency dependence in the numerical approximation.

The intent of this paper is to investigate the effectiveness of direct numerical computation in capturing acoustic fields. It has been the trend to use high-order schemes whenever there is interest in resolving the acoustic field, even though there has never been a complete study of the accuracy of low-order schemes. We revisit a long-standing benchmark problem in aeroacoustics to show the validity of such low-order schemes. The problem we consider is that of a flat-plate airfoil in a non-uniform flow. We show that when the linearized Euler equations are used to model problems in aeroacoustics, a simple second-order numerical scheme is powerful enough to provide accurate aeroacoustic results. We validate this computational approach by comparing both the RMS and instantaneous pressure on the airfoil and in the far field to semianalytic and asymptotic results.

In this paper we consider the scattering of sound by two- and three-dimensional bodies with arbitrary geometries. Particular emphasis is placed on the methodology for the implementation of solid wall boundary conditions for high-order, high-bandwidth numerical schemes. The Impedance Mismatch Method (IMM) is introduced to treat solid wall boundaries. In this method the solid wall is simulated using a wall region in which the characteristic impedance is set to a different value from that in the fluid region. This method has many advantages over traditional solid wall boundary treatments, including simplicity of coding, speed of computation and the ability to treat curved boundaries. This method has been used to solve a number of acoustic scattering problems to demonstrate its effectiveness. These problems include acoustic reflections from an infinite plate, acoustic scattering from a two-dimensional finite plate and a cylinder, and acoustic scattering by a sphere and a cylindrical shell.