An efficient discontinuous Galerkin method for aeroacoustic propagation

An efficient discontinuous Galerkin formulation is applied to the solution of the linearized Euler equations and the acoustic perturbation equations for the simulation of aeroacoustic propagation in two-dimensional and axisymmetric problems, with triangular and quadrilateral elements. To improve computational efficiency, a new strategy of variable interpolation order is proposed in addition to a quadrature-free approach and parallel implementation. Moreover, an accurate wall boundary condition is formulated on the basis of the solution of the Riemann problem for a reflective wall. Time discretization is based on a low dissipation formulation of a fourth-order, low storage Runge-Kutta scheme. Along the far-field boundaries a perfectly matched layer boundary condition is used. For the far-field computations, the integral formulation of Ffowcs Williams and Hawkings is coupled with the near-field solver. The efficiency and accuracy of the proposed variable order formulation is assessed for realistic geometries, namely sound propagation around a high-lift airfoil and the Munt problem

On adomian based numerical schemes for euler and navier-stokes equations, and application to aeroacoustic propagation

140 p.En esta tesis se ha desarrollado un nuevo método de integración en tiempo de tipo derivadas sucesivas (multiderivative), llamado ABS y basado en el algoritmo de Adomian. Su motivación radica en la reducción del coste de simulación para problemas en aeroacústica, muy costosos por su naturaleza transitoria y requisitos de alta precisión. El método ha sido satisfactoriamente empleado en ambas partes de un sistema híbrido, donde se distinguen la parte aerodinámica y la acústica.En la parte aerodinámica las ecuaciones de Navier-Stokes incompresibles son resueltas con unmétodo de proyección clásico. Sin embargo, la fase de predicción de velocidad ha sido modificadapara incluir el método ABS en combinación con dos métodos: una discretización espacial MAC devolúmenes finitos, y también con un método de alto orden basado en ADER. El método se ha validado respecto a los problemas (en 2D) de vórtices de Taylor-Green, y el desarrollo de vórticesde Karman en un cilindro cuadrado. La parte acústica resuelve la propagación de ondas descritaspor las ecuaciones linearizadas de Euler, empleando una discretización de Galerkin discontinua. El método se ha validado respecto a la ecuación de Burgers.El método ABS es sencillo de programar con una formulación recursiva. Los resultados demuestran que su sencillez junto con sus altas capacidades de adaptación lo convierten en un método fácilmente extensible a órdenes altos, a la vez que reduce el coste comparado con otros métodos clásicos

On Adomian Based Numerical Schemes for Euler and Navier-Stokes Equations, and Application to Aeroacoustic Propagation

In this thesis, an Adomian Based Scheme (ABS) for the compressible Navier-Stokes equations is constructed, resulting in a new multiderivative type scheme not found in the context of fluid dynamics. Moreover, this scheme is developed as a means to reduce the computational cost associated with aeroacoustic simulations, which are unsteady in nature with high-order requirements for the acoustic wave propagation. We start by constructing a set of governing equations for the hybrid computational aeroacoustics method, splitting the problem into two steps: acoustic source computation and wave propagation. The first step solves the incompressible Navier-Stokes equation using Chorin's projection method, which can be understood as a prediction-correction method. First, the velocity prediction is obtained solving the viscous Burgers' equation. Then, its divergence-free correction is performed using a pressure Poisson type projection. In the velocity prediction substep, Burgers' equation is solved using two ABS variants: a MAC type implementation, and a ``modern'' ADER method. The second step in the hybrid method, related to wave propagation, is solved combining ABS with the discontinuous Galerkin high-order approach. Described solvers are validated against several test cases: vortex shedding and Taylor-Green vortex problems for the first step, and a Gaussian wave propagation in the second case. Although ABS is a multiderivative type scheme, it is easily programmed with an elegant recursive formulation, even for the general Navier-Stokes equations. Results show that its simplicity combined with excellent adaptivity capabilities allows for a successful extension to very high-order accuracy at relatively low cost, obtaining considerable time savings in all test cases considered.Predoc Gobierno Vasc

Application and assessment of time-domain DGM for intake acoustics using 3D linearized Euler equations

Fan noise is one of the major sources of aircraft noise. This can be modelled by means of frequency and time domain CAA methods. Frequency domain methods based on the convected Helmholtz equation are widely used for noise propagation and radiation from turbofan intakes. However, these methods are unsuited to deal easily with turbofan exhaust noise and presently unable to solve large 3D (three-dimensional) problems at high frequencies. In this thesis the application of time-domain Discontinuous Galerkin Methods (DGM) for solving linearized Euler equations is investigated. The research is focused on large 3D problems with arbitrary mean flows. A commercially available DGM code, Actran DGM, is used.An automatic procedure has been developed to perform the DGM simulations for axisymmetric and 3D intake problems by providing simple control of all the parameters (flow, geometry, liners). Moreover, a new method for integrating source predictions obtained from CFD calculations for the fan stage of a turbofan engine with the DGM code to predict tonal noise radiation in the far field has been proposed, implemented and validated.The DGM is validated and benchmarked for intake and exhaust problems against analytical solutions and other numerical methods. The principal properties of the DGM are assessed, best practice is defined, and important issues which relate to the accuracy and stability of the liner model are identified. The accuracy and efficiency of the CFD/CAA coupling are investigated and results obtained are compared to rig test data.The influence of the 3D intake shapes and the mean flow distortion on the sound field is investigated for static rig and flight conditions by using the DGM approach. Moreover, it is shown that the mean flow distortion can have a significant effect on the sound attenuation by a liner

An unstructured numerical method for computational aeroacoustics

The successful application of Computational Aeroacoustics (CAA) requires high accuracy numerical schemes with good dissipation and dispersion characteristics. Unstructured meshes have a greater geometrical flexibility than existing high order structured mesh methods. This work investigates the suitability of unstructured mesh techniques by computing a two-dimensionallinearised Euler problem with various discretisation schemes and different mesh types. The goal of the present work is the development of an unstructured numerical method with the high accuracy, low dissipation and low dispersion required to be an effective tool in the study of aeroacoustics. The suitability of the unstructured method is investigated using aeroacoustic test cases taken from CAA Benchmark Workshop proceedings. Comparisons are made with exact solutions and a high order structured method. The higher order structured method was based upon a standard central differencing spatial discretisation. For the unstructured method a vertex-based data structure is employed. A median-dual control volume is used for the finite volume approximation with the option of using a Green-Gauss gradient approximation technique or a Least Squares approximation. The temporal discretisation used for both the structured and unstructured numerical methods is an explicit Runge-Kutta method with local timestepping. For the unstructured method, the gradient approximation technique is used to compute gradients at each vertex, these are then used to reconstruct the fluxes at the control volume faces. The unstructured mesh types used to evaluate the numerical method include semi-structured and purely unstructured triangular meshes. The semi-structured meshes were created directly from the associated structured mesh. The purely unstructured meshes were created using a commercial paving algorithm. The Least Squares method has the potential to allow high order reconstruction. Results show that a Weighted Least gradient approximation gives better solutions than unweighted and Green-Gauss gradient computation. The solutions are of acceptable accuracy on these problems with the absolute error of the unstructured method approaching that of a high order structured solution on an equivalent mesh for specific aeroacoustic scenarios