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Showing papers on "Computational aeroacoustics published in 2018"


Journal ArticleDOI
TL;DR: In this paper, the impact of porous surfaces on the near-wall turbulent structures and the generated trailing-edge noise is analyzed for several trailing edge shapes of finite thickness using a high resolution large-eddy simulation (LES)/computational aeroacoustics (CAA) method.

38 citations


Journal ArticleDOI
TL;DR: A comprehensive overview of the research activities on wind turbine aeroacoustics at DTU over the last 20 years is provided, as well as the state-of-the-art of noise prediction models for wind turbines under complex inflow conditions are given.
Abstract: The present review paper provides a comprehensive overview of the research activities on wind turbine aeroacoustics at DTU over the last 20 years, as well as it gives the state-of-the-art of noise prediction models for wind turbines under complex inflow conditions. Various noise generation models developed at DTU are described and analyzed, including models based on the acoustic analogy, flow-acoustics splitting techniques, Amiet's model, and various engineering models. Some of the models are coupled to existing aero-elastic software and computational fluid mechanics models developed at DTU, and implemented in the simulation platform WindSTAR (Wind turbine Simulation Tool for AeRodynamic noise). This simulation platform consists of WindSTAR-Gen, dealing with models for generation of noise and design of low-noise wind turbines, and WindSTAR-Pro, which is developed to handle the modeling of long distance acoustic propagation. As specific features of the WindSTAR-Pro package, the rotation of the noise sources is modeled, the propagation simulations combine the so-called Parabolic Equations (PE) propagation model with numerical flow simulations to take into account effects from wind turbine wakes, atmospheric turbulence and wind shear.

33 citations


Journal ArticleDOI
TL;DR: In this paper, a hybrid computational aero-acoustics method is applied to investigate the effect of wavy leading edges on rod-airfoil interaction noise, and the flow field is solved by an incompressible large-eddy simulator.
Abstract: A hybrid computational aeroacoustics method is applied to investigate the effect of wavy leading edges on rod–airfoil interaction noise. The flow field is solved by an incompressible large-eddy sim...

30 citations


Journal ArticleDOI
TL;DR: In this paper, a detailed model of the nose section of a 90-seat configuration green regional aircraft concept was built and a nose landing-gear test campaign was conducted to evaluate its performance.
Abstract: This paper presents experimental results from a nose landing-gear test campaign. A highly detailed model of the nose section of a 90-seat configuration green regional aircraft concept was built and...

25 citations


Journal ArticleDOI
TL;DR: The novel Delayed-Time Domain Impedance Boundary Condition (D-TDIBC) technique developed to impose a time delay to acoustic wave reflection to provide acoustically well-posed boundary conditions in compressible Navier–Stokes simulations is presented.

20 citations


Journal ArticleDOI
TL;DR: In this article, the aerodynamic field around a FX 63-137 airfoil for four angles of attack and low Reynolds numbers was simulated with a Large Eddy Simulation (LES).

19 citations


Journal ArticleDOI
TL;DR: In this paper, a new extension to the Random Particle Mesh (RPM) method was introduced, which accommodates in-depth studies of the impact of cyclostationary wake characteristics on the broadband noise in the fan stage.

18 citations


Journal ArticleDOI
TL;DR: In this article, the impact of porous material with variable properties on trailing edge noise is analyzed by a high resolution large-eddy simulation/computational aeroacoustics (LES/CAA) approach.

17 citations



Proceedings ArticleDOI
25 Jun 2018
TL;DR: In this paper, a 3D CAA (Computational Aeroacoustics) code is used to solve the linearized-Euler equations applied to the disturbances and coupled with a synthetic turbulence injection model.
Abstract: Turbulent RSI (rotor-stator interaction) mechanism is a major broadband source contribution of turbofan noise generation. Acoustic prediction tools used by Industry are based on flat-plate cascade response models with restrictive assumptions on flow and geometry. Due to huge CPU memory and time cost required, Large Eddy Simulations of the complete fan-OGV stage are still out of reach (apart from recent impressive results obtained using the Lattice Boltzmann Method). This paper presents an alternative approach based on the use of a 3-D CAA (Computational Aeroacoustics) code solving the linearized-Euler equations applied to the disturbances and coupled with a synthetic turbulence injection model. The inflow turbulence is synthetized by means of a sum of harmonic gusts with random phases. The Fourier-mode amplitudes are trimmed by a 2 or 3-wave number Von-Karman or Liepmann turbulence spectrum. Swirling convection of the synthetic turbulence is provided by a 3D RANS mean flow solution and interpolated at the nodes of the CAA grid. In this paper, our methodology is first validated on a benchmark case (fully annular duct with swirling flow and a prescribed turbulence) and then applied for the first time to an industrial turbofan in the framework of a European project, TurboNoiseBB. Previous implemented 2D formulation (2-wave number spectrum) for turbulence generation is extended here to 3D (axial, radial, and angular modes) in order to study the sensitivity on cascade effects.

12 citations


Journal ArticleDOI
TL;DR: A new meshless approach based on a Galerkin discretization of a set of conservation equations on an Arbitrary Lagrangian–Eulerian framework, which allows using all the advantages of the Lagrangia approaches in the context of Computational Aeroacoustics.

Journal ArticleDOI
TL;DR: In this paper, a frequency-domain methodology for acoustic scattering prediction from rotating sources is suggested, which can be coupled to any boundary method which requires a solution of the incident field on the hardwall scattering surface.

Journal ArticleDOI
TL;DR: In this article, a numerical investigation on the influence of structural flexibility and flow velocity on the flow-induced acoustic and vibration response of a plate is presented, where simulations are performed on a te...
Abstract: A numerical investigation on the influence of structural flexibility and flow velocity on the flow-induced acoustic and vibration response of a plate is presented. Simulations are performed on a te...

Journal ArticleDOI
TL;DR: In modern aeroengines, combustion noise has become a significant source to the overall noise, particularly at approach conditions, and this requires further advances in understanding and predicting combustion noise as discussed by the authors.
Abstract: In modern aeroengines, combustion noise has become a significant source to the overall noise, particularly at approach conditions. This requires further advances in understanding and predicting com...

Journal ArticleDOI
TL;DR: A separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.

Journal ArticleDOI
TL;DR: A new methodology for the numerical estimation of the Green’s functions in complex external aeroacoustic configurations is presented.
Abstract: The Paper presents a new methodology for the numerical estimation of the Green’s functions in complex external aeroacoustic configurations. Computational aeroacoustics is used to propagate multifre...

Journal ArticleDOI
TL;DR: In this paper, the authors simulate numerically the flow and noise on the Advanced Noise Control Fan (ANCF) to predict accurately the tonal noise as well as the broadband content of the ducted rotor/stator model using as a reference the provided far-field noise measurements.
Abstract: The purpose is to simulate numerically the flow and noise on the Advanced Noise Control Fan (ANCF). The ANCF model was developed by the NASA Glenn Research Center to provide measurement data of a turbofan flow and its corresponding generated noise. The aim of the numerical simulations is to predict accurately the tonal noise as well as the broadband content of the ducted rotor/stator model using as a reference the provided far-field noise measurements.

Journal ArticleDOI
TL;DR: In this paper, a set of large eddy simulations is used to perform a numerical analysis of fluidic injection as a tool for noise reduction, which allows on-line noise reduction.
Abstract: A set of large eddy simulations is used to perform a numerical analysis of fluidic injection as a tool for noise reduction. This technique, developed at the Pennsylvania State University, allows on...

Posted ContentDOI
01 Jan 2018
TL;DR: It is found that the recirculating flows are associated with the gap between the shroud and the inlet duct, and the magnitudes of the tonal noise at the blade passing frequencies are well predicted.
Abstract: In this study, tonal noise from an isolated centrifugal fan is investigated using unsteady Reynolds-averaged Navier-Stokes (URANS) simulations. Isolated centrifugal fans are often used in ventilation systems and play an important role in producing tonal and broadband noise. The broadband noise can be reduced when the fan efficiency is optimized. However, the tonal noise cannot be effectively reduced. It is therefore of great interest to identify and reduce the tonal noise for this type of fans operating in public environment. The noise is predicted by coupling the URANS and the Ffowcs Williams and Hawkings acoustic analogy. The numerical methodology and mesh generation methods are validated. Numerical simulation is a more convenient way to identify tonal noise than experiments. However, simulation of the noise using advanced computational fluid dynamics (CFD) methods (e.g., large eddy simulation) requires many computational resources. To predict the tonal noise, a potentially convenient method is the URANS. The method can simulate characteristic unsteady structures, which are responsible for the tonal noise generation, with low computational costs. Though it has a drawback to provide the fluctuations that are important for the broadband noise generation. The aerodynamic properties obtained from RANS and URANS are consistent with the experimental data. The magnitudes of the tonal noise at the blade passing frequencies are well predicted. Moreover, the broadband noise below 350 Hz agrees with the measurement although obvious discrepancies are found at high frequencies, which cannot be resolved by URANS. Recirculating flows, which are responsible for reducing the fan efficiency and increasing the noise generation, are observed between the shroud and the blade trailing edges. It is found that the recirculating flows are associated with the gap that is between the shroud and the inlet duct.

Journal ArticleDOI
TL;DR: In this article, a modified Weight Essentially Non-Oscillatory (WENO) scheme is proposed at the interfaces of multi-block grids to deal with CAA multi-scale problems.

Proceedings ArticleDOI
08 Jan 2018
TL;DR: In this paper, a Computational Aeroacoustics (CAA) platform for CRORs based on the Harmonic Balance method is presented and is applied to a generic, full scale, pusher type CROR operating at cruise conditions.
Abstract: The Counter Rotating Open Rotor (CROR) powerplant is an interesting architecture for future regional aircraft propulsion since it offers higher propulsive efficiency and thereby lower fuel consumption than the conventional Turbofan engine. The noise levels generated are however potentially larger compared to a Turbofan due in part to the absence of a ducting nacelle. This raises the need for efficient, high fidelity tools that can be used for the design and evaluation of new blade concepts capable of meeting strict noise regulations. In this paper, a Computational Aeroacoustics (CAA) platform for CRORs based on the Harmonic Balance method is presented. The method is formulated in the time domain and solves for the dominant frequencies of the flow by expressing the solution as a truncated Fourier series in time. Coupling between the resolved frequencies is furthermore possible since the nonlinear URANS equations are solved for. The far field acoustic signature is obtained by solving a convective form of the Ffowcs Williams-Hawkings equations for permeable surfaces. The CAA platform is applied to a generic, full scale, pusher type CROR operating at cruise conditions.

Dissertation
01 Jan 2018
TL;DR: A hybrid Computational Aeroacoustics (CAA) method is devised, implemented and applied to two enclosed, reactive configurations in this work, focused on stability and flexibility to allow for an easy adaption to industrial applications, such as combustion noise.
Abstract: Future air traffic regulations are going to further limit the noise and pollutant emissions of aero engines in a way that can only be met by the comprehensive migration towards lean premixed combustion based aero engine designs Compared to conventional rich-quench-lean setups, these next generation combustion systems are more prone to thermoacoustic instabilities caused by combustion noise For this reason, improved methods for the prediction and investigation of combustion noise and thermoacoustic instabilities are required Consequently, a hybrid Computational Aeroacoustics (CAA) method is devised, implemented and applied to two enclosed, reactive configurations in this work The method comprises a low Mach number flow solver, a dedicated acoustics tool and a coupling layer, which bridges the different numerical schemes and physical phenomena In addition to traditional aeroacoustic problems, the method is applicable to enclosed configurations with complex geometries, while maintaining the favorable computational efficiency of common hybrid methods Its key components are the newly developed acoustics solver and the corresponding coupling layer For the description of the reacting flow field, an established, finite volume based flow solver is equipped with the coupling interface By employing the high order spectral/hp element method in a discontinuous Galerkin formulation, the CAA solver efficiently accounts for acoustic wave propagation in complex, three-dimensional geometries Its implementation is focused on stability and flexibility to allow for an easy adaption to industrial applications, such as combustion noise This is achieved by solving the unconditionally stable Acoustic Perturbation Equations (APE) and using a set of Riemann solvers that can operate on variable density base flows The developed coupling layer enables bi-directional communication of both solvers at run-time, without limiting their spatial and temporal resolutions, even when applied to coinciding domains Their different length scales and discretization methods are overcome by a linear interpolation in time and a spatial, implicit low pass filter, that operates on an intermediate representation of the flow fields The applicability of the hybrid CAA method is investigated by means of two laboratory scale combustors of increasing complexity The first setup features a half-dump combustor, that facilitates a basic validation of the CAA solver and the coupling It is shown that the short length scale base flow fields are sufficiently represented in terms of the CAA expansion by the coupling layer In the obtained acoustic fields, the behavior of the system's first eigenmode is well reproduced The instigation of a second eigenmode was not observed in the experimental noise spectrum but is in agreement with a similar hybrid CAA simulation The second configuration is a pressurized burner, operated by a swirl stabilized, premixed flame It is already beyond the capabilities of most available CAA tools and features most phenomena present in industry scale combustion systems In the considered frequency range, the prevalent eigenmode is very well predicted Independent of the acoustic governing equations, the developed method is estimated to require less than a fifth of the computational effort of a direct noise simulation for the considered configuration

Dissertation
16 Oct 2018
TL;DR: In this paper, the authors define admissibility conditions for nonlinear TDIBCs under the impedance, admittance, and scattering formulations, and show that linear physical models, whose Laplace transforms are irrational, admit in the time domain a time-delayed oscillatory-diffusive representation and give its physical interpretation.
Abstract: In computational aeroacoustics, time-domain impedance boundary conditions (TDIBCs) can be employed to model a locally reacting sound absorbing material. They enable to compute the effect of a material on the sound field after a homogenization distance and have proven effective in noise level predictions. The broad objective of this work is to study the physical, mathematical, and computational aspects of TDIBCs, starting from the physical literature. The first part of this dissertation defines admissibility conditions for nonlinear TDIBCs under the impedance, admittance, and scattering formulations. It then shows that linear physical models, whose Laplace transforms are irrational, admit in the time domain a time-delayed oscillatory-diffusive representation and gives its physical interpretation. This analysis enables to derive the discrete TDIBC best suited to a particular physical model, by contrast with a one-size-fits-all approach, and suggests elementary ways of computing the poles and weights. The proposed time-local formulation consists in composing a set of ordinary differential equations with a transport equation. The main contribution of the second part is the proof of the asymptotic stability of the multidimensional wave equation coupled with various classes of admissible TDIBCs, whose Laplace transforms are positive-real functions. The method of proof consists in formulating an abstract Cauchy problem on an extended state space using a realization of the impedance, be it finite or infinite-dimensional. The asymptotic stability of the corresponding strongly continuous semigroup of contractions is then obtained by verifying the sufficient spectral conditions of the Arendt-Batty-Lyubich-Vũ theorem. The third and last part of the dissertation tackles the discretization of the linearized Euler equations with TDIBCs. It demonstrates the computational advantage of using the scattering operator over the impedance and admittance operators, even for nonlinear TDIBCs. This is achieved by a systematic semi-discrete energy analysis of the weak enforcement of a generic nonlinear TDIBC in a discontinuous Galerkin finite element method. In particular, the analysis highlights that the sole definition of a discrete model is not enough to fully define a TDIBC. To support the analysis, an elementary physical nonlinear scattering operator is derived and its computational properties are investigated in an impedance tube. Then, the derivation of time-delayed broadband TDIBCs from physical reflection coefficient models is carried out for single degree of freedom acoustical liners. A high-order discretization of the derived time-local formulation, which consists in composing a set of ordinary differential equations with a transport equation, is applied to two flow ducts.

Journal ArticleDOI
TL;DR: This study aims to examine the aerodynamics and aeroacoustics performance of an open system consisting of an axial fan and a heat exchanger where hybrid method incorporating CFD and CAA is used to predict the noise behavior.
Abstract: An accurate noise prediction is important in order to reduce noise emission significantly and to prevent expensive after-design treatments. This study aims to examine the aerodynamics and aeroacoustics performance of an open system consisting of an axial fan and a heat exchanger where hybrid method incorporating CFD (Computational Fluid Dynamics) and CAA (Computational Aeroacoustics) is used to predict the noise behavior. The hybrid model method used consists of three steps. Firstly, the flow is computed by means of flow-computed fluids and the pressure fluctuations are obtained. This is followed by the acquisition of acoustic signals from these fluctuations and the attainment of a sound pressure level approach with the FW-H (Ffowcs Williams & Hawkings) model. Unsteady flow field of the air channel case was obtained by using different turbulence models. The SAS model is capable of resolving largescale turbulent structures without the time and grid-scale resolution restrictions of LES (Large Eddy Simulations), often allowing the use of existing grids created for URANS simulations. For this reason, two different turbulence models, namely URANS (Unsteady Reynolds Averaged Navier Stokes) model, SAS (Scale Adaptive Simulations) model have been applied. Acoustic sources were computed based on the pressure fluctuations and sound pressure level and frequency dependent graphics were plotted with Fast Fourier Transform. On the other hand, acoustic measurements were performed in a semi-anechoic chamber for both of them. When the experimental and numerical results were compared with the previously determined receiver points, the accuracy rate was obtained as SAS, URANS respectiv ely.

Journal ArticleDOI
TL;DR: Uncertainty quantification has been achieved for the noise propagation stage of hybrid CAA, and also on the noise prediction of a non-lifting helicopter rotor in hover, showing that the source of the uncertainty in the noise is dominated by the major characteristic properties of the simulations.

Dissertation
23 Feb 2018
TL;DR: The whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference and a novel remeshing strategy with conservative interpolation between meshes is presented.
Abstract: The solution of the human phonation problem applying computational mechanics is covered by several research branches, such as Computational Fluid Dynamics (CFD), biomechanics or acoustics, among others. In the present thesis, the problem is approached from the Computational Aeroacoustics (CAA) point of view and the first main objective consists in developing numerical methods of general application that can take part in the solution of any scenario related to human phonation with a reasonable cost. In this sense, only the compressible Navier-Stokes equations can describe all flow and acoustic scales without any modeling, which is known as Direct Numerical Simulation (DNS), but its computational cost is usually unaffordable. Even in the case of a Large Eddy Simulation (LES), where the small scales are modeled, the cost can still be a handicap due to the complexity of the problem. This drawback gets worse in the low Mach regime due to the large disparity between flow velocity and sound speed, which leads to an ill-conditioning of the system of equations, specially for conservative schemes. At this point, it makes sense to move towards the incompressible flow approximation, bearing in mind the low velocities expected in human phonation problems. Incompressible flows do not yield any acoustics, for which a second problem containing the propagation of the sound sources needs to be modeled and solved. These are the so called hybrid methods, which allow a better conditioning of the problem by segregating flow and acoustic scales. Lighthill's analogy has been taken as starting point for the present work, but its restriction to free-field scenarios has motivated the extension of the method to arbitrary geometries and non-uniform flows. The first development in this direction consists in a splitting of Lighthill's analogy into a quadrupolar and dipolar component, which does not change the original problem but allows assessing the contribution of solid boundaries to the generation of sound. The second step consists in the development of a stabilized Finite Element (FEM) formulation for the Acoustic Perturbation Equations (APE) which account for non-uniform flows and perform a complete filtering of the acoustic scales. The final step assumes the compressible approach but omitting the energy equation and thus considering both flow and acoustic propagation as isentropic. In this case the solver is unified and hence a method for applying compatible boundary conditions for flow and acoustics has been developed. Moreover, the whole numerical framework has been extended to dynamic phonation cases, which require using an Arbitrary Lagrangian Eulerian (ALE) reference. Also, a novel remeshing strategy with conservative interpolation between meshes is presented. In the last chapter a challenging case in human phonation has been chosen for testing the developed computational framework: the fricative phoneme /s/. Unlike vowels, which are voiced sounds defined by a few characteristic frequencies, fricatives cannot be simulated as the propagation of a known analytic solution (glottal pulse) because the sound sources correspond to a wide range of turbulent scales. Therefore, a CFD calculation is mandatory in order to capture all relevant eddies behind the generation of sound. This problem is solved with an LES together with the Variational Multiscale (VMS) stabilization method as turbulence model, which is supplemented with several acoustic formulations when using incompressible flow. The analysis of the results focuses on the numerical representation of turbulence and the acoustic signal at the far-field, which has been compared to experimental recordings. Finally, the role of the upper incisors in the generation of the fricative sound has been evaluated. All simulations have been run with the parallel multiphysics FEM code FEMUSS, based on FORTRAN Object-Oriented-Programming land the OpenMPI parallel library.

Journal ArticleDOI
TL;DR: The nonlinear filter of Yee & Sjogreen with shock-capturing and long time integration capabilities is used to replace the standard DRP linear filter for both smooth flows and flows containing discontinuities.

Proceedings Article
01 Mar 2018
TL;DR: It is proposed that machine learning can effectively predict the noise generated by a coaxial jet exhaust by utilizing a database of computational experiments that cover a variety of flow and geometric configurations.
Abstract: This paper presents a preliminary method for improving the design and development process in a way that combines engineering design approaches based on learning algorithms and computational aeroacoustics. It is proposed that machine learning can effectively predict the noise generated by a coaxial jet exhaust by utilizing a database of computational experiments that cover a variety of flow and geometric configurations. A conceptual framework has been outlined for the development of a practical design tool to predict the changes in jet acoustics imparted by varying the fan nozzle geometry and engine cycle of a coaxial jet. It is proposed that computational aeroacoustic analysis is used to generate a training and validation database for an artificial neural network. The trained network can then predict noise data for any operational configuration. This method allows for the exploration of noise emissions from a variety of fan nozzle areas, engine cycles and flight conditions. It is intended that this be used as a design tool in order to reduce the design cycle time of new engine configurations and provide engineers with insight into the relationship between jet noise and the input variables.

Journal ArticleDOI
TL;DR: The goal of the present study were to provide a suitable methodology for aeroacoustic optimization by means of numerical analyses using commercial computational fluid dynamics tools (Ansys Fluent), and the application of a detached splitter plate in the turbulent wake of a circular cylinder as a passive control method for noise generation was investigated.
Abstract: Computational aeroacoustics simulations require a considerable amount of time, which makes the comparison of a large number of different geometric designs a difficult task. The goal of the present study were to provide a suitable methodology for aeroacoustic optimization. By means of numerical analyses using commercial computational fluid dynamics tools (Ansys Fluent), the application of a detached splitter plate in the turbulent wake of a circular cylinder as a passive control method for noise generation was investigated. We have employed two-dimensional URANS simulations, so this case can be considered a toy problem, which contains the main challenges of the physical problem and could indicate trends correctly, but was simplified in order to decrease the computational cost to an affordable level, at the cost of making comparison with experimental data not possible. The irradiation of noise caused by the interaction between the flow and both bodies was evaluated using computational aeroacoustics tools based on the Ffowcs-Williams and Hawkings method. Using a commercial optimization software package (modeFRONTIER), various design optimization methodologies were applied to this flow in order to achieve a possible optimal configuration, i.e., one which is capable of reducing the far field noise level without increasing the aerodynamic forces. Using a multi-objective optimization tool, it was possible to evaluate the behavior of heuristic optimization algorithms and the major advantage of algorithms based on response surface methods when applied to a nonlinear aeroacoustics problem, since they require a smaller number of calculated designs to reach the optimal configuration. In addition, we applied a partitive clustering technique to identify and group the cases simulated into five clusters based on their geometric parameters, overall sound pressure level and RMS of the drag coefficient, confirming the efficiency of the application of long detached splitter plates placed next to the cylinder in stabilizing the turbulent wake, whereas the positioning of splitter plates at a distance larger than a critical gap increased the overall sound pressure level radiated due to the formation of vortices in the gap.

Proceedings ArticleDOI
25 Jun 2018
TL;DR: In this paper, an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Yw = 1/Zw, is derived and coupled with a time domain boundary integral equation.
Abstract: Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance, Z(w). Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic wave scattering of geometric bodies treated with acoustic liners. This work uses an admittance boundary condition where the admittance, Y(w), is defined to be the inverse of impedance, i.e., Y(w) = 1/Z(w). An admittance boundary condition will be derived and coupled with a time domain boundary integral equation. The solution will be obtained iteratively using spatial and temporal basis functions and will allow for acoustic scattering problems to be modeled with geometries consisting of both unlined and soft surfaces. Stability will be demonstrated through eigenvalue analysis.