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We introduce a family of impulselike methods for the integration of highly oscillatory second-order differential equations whose forces can be split into a fast part and a slow part. Methods of this family are specified by two weight functions Φ, ψ; one is used to average positions and the other to mollify the force. When the fast forces are conservative and Φ = ψ, the methods here coincide with the mollified impulse methods introduced by García-Archilla, Sanz-Serna, and Skeel. On the other hand, the methods here extend to nonlinear situations a well-known class of exponential integrators introduced by Hairer and Lubich for cases of linear fast forces. A convergence analysis is presented that provides insight into the role played by the processes of mollification and averaging in avoiding order reduction. A simple condition on the weight functions is shown to be both necessary and sufficient to avoid order reduction. [ABSTRACT FROM AUTHOR]

Abstract: A fourth-order numerical method for the zero-Mach-number limit of the equations for compressible flow is presented. The method is formed by discretizing a new auxiliary variable formulation of the conservation equations, which is a variable density analog to the impulse or gauge formulation of the incompressible Euler equations. An auxiliary variable projection method is applied to this formulation, and accuracy is achieved by combining a fourth-order finite-volume spatial discretization with a fourth-order temporal scheme based on spectral deferred corrections. Numerical results are included which demonstrate fourth-order spatial and temporal accuracy for non-trivial flows in simple geometries. [Copyright &y& Elsevier]

Acoustic louvres are commonly used to provide natural ventilation while offering some reduction of noise break-in from external sources or control of noise break-out from machinery in the building. The sound insulation of acoustic louvres is not high, particularly at low frequencies, and therefore can be the dominant contribution to the overall performance of a fac¸ade or acoustic enclosure. Developments in acoustic louvre design have been hindered by the lack of an agreed simple measurement method that allows the effectiveness of prototypes to be assessed. In a companion paper, a method has been proposed for the direct measurement of the sound transmission loss of louvres by an impulse method, which circumvents the limitations imposed by standard methods. However, the field performance of louvres is more properly characterised by the sound insertion loss, rather than transmission loss, and a question remains on how impulse data can be transformed to predict field performance. In the present paper a description is given of the derivation of a transformation based on an image model of a test chamber with aperture. The resultant output data is in a form expected from measurements of insertion loss and includes directivity. The impulse measurement technique, combined with the transformation, promises an inexpensive method of assessing field performance of louvres without recourse to specialist acoustic test facilities. [Copyright &y& Elsevier]