260 research outputs found
The partition of unity finite element method for short wave acoustic propagation on non-uniform potential flows
No full textA novel numerical method is proposed for modelling time-harmonic acoustic propagation of short wavelength disturbances on non-uniform potential flows. The method is based on the partition of unity finite element method in which a local basis of discrete plane waves is used to enrich the conventional finite element approximation space. The basis functions are local solutions of the governing equations. They are able to represent accurately the highly oscillatory behaviour of the solution within each element while taking into account the convective effect of the flow and the spatial variation in local sound speed when the flow is non-uniform. Many wavelengths can be included within a single element leading to ultra-sparse meshes. Results presented in this article will demonstrate that accurate solutions can be obtained in this way for a greatly reduced number of degrees of freedom when compared to conventional element or grid-based schemes. Numerical results for lined uniform two-dimensional ducts and for non-uniform axisymmetric ducts are presented to indicate the accuracy and performance which can be achieved. Numerical studies indicate that the pollution effect associated with cumulative dispersion error in conventional finite element schemes is largely eliminated
A comparison of two Trefftz-type methods: the ultraweak variational formulation and the least-squares method, for solving shortwave 2-D Helmholtz problems
No full textTrefftz methods for the numerical solution of partial differential equations (PDEs) on a given domain involve trial functions which are defined in subdomains, are generally discontinuous, and are solutions of the governing PDE (or its adjoint) within each subdomain. The boundary conditions and matching conditions between subdomains must be enforced separately. An interesting novel result presented in this paper is that the least-squares method (LSM) and the ultraweak variational formulation, two methods already established for solving the Helmholtz equation, can be derived in the framework of the Trefftz-type methods. In the first case, the boundary conditions and interelement continuity are enforced by means of a least-squares procedure. In the second, a Galerkin-type weighted residual method is used. Another goal of the work is to assess the relative efficiency of each method for solving shortwave problems in acoustics and to study the stability of each method. The numerical performance of each scheme is assessed with reference to two 2-D test problems; acoustic propagation in an uniform soft-walled duct, and propagation in an L-shaped domain, the latter involving singular behaviour at a sharp corner
The partition of unity finite element method for short wave acoustic propagation on non-uniform potential flows
No full textSpecial short wave elements for flow acoustics
No full textA numerical formulation based on the Partition of Unity Method (PUM) is proposed for modelling the propagation of short acoustic waves on irrotational mean flows. The method seeks to reduce the pollution error which exists in conventional FE schemes at high frequencies by using a local basis which is enriched by plane wave solutions of the convected Helmholtz equation. Initially the method is demonstrated with reference to a one dimensional model consisting of a variable area converging-diverging duct with mean flow. Next a simple two-dimensional model of a straight duct with uniform flow, is considered. In both cases the accuracy and the conditioning of the numerical solution is investigated for ranges of frequency and Mach number characteristic of aero-engine bypass ducts
Special short wave finite elements for flow acoustics
No full textA numerical scheme based on the Partition of Unity Finite Element Method is proposed for solving shortwave problems in flow acoustics. The goal of this approach is to obtain accurate solutions with fewer degrees of freedom than are required for conventional grid or node based schemes. Preliminary numerical results obtained for 2-D and axisymmetric models indicate that this approach may offer significant performance improvements
De cuarentenas, encierros y violencias: Las acciones colectivas de violencia punitiva en Argentina durante 2020
No full textEl 11 de marzo de 2020 la Organización Mundial de la Salud declaró a la enfermedad del Covid-19 como una pandemia de escala planetaria. Durante los meses subsiguientes la propagación del virus se haría sentir en prácticamente todos los rincones del mundo, provocando no solo la pérdida de innumerables vidas sino el trastocamiento de la existencia cotidiana de millones de personas. Argentina no ha sido la excepción a este proceso y el tránsito del país por la pandemia ha dejado huellas visibles en diversas dimensiones de lo social. En este texto nos proponemos analizar el impacto de estas transformaciones sobre la dinámica de las violencias, particularmente sobre la evolución de las acciones colectivas de violencia punitiva durante el año 2020. Este trabajo se inscribe y continúa investigaciones previas de nuestra autoría que han abordado el desarrollo de dichas acciones para los años 1997-2008 (González et al., 2011) y 2009-2015 (Gamallo, 2017 y 2020). En línea con esas publicaciones, se trabajará con una estrategia metodológica de carácter cuantitativo, diseñada a partir del procesamiento estadístico de una base de datos conformada con todos los episodios de violencia colectiva punitiva hallados en la prensa nacional y local desde el 1 de enero hasta el 31 de diciembre de 2020. Buscamos comparar los datos de 2020 con años previos, con el objetivo de conocer los efectos de la pandemia y de las distintas medidas gubernamentales sobre un fenómeno particular como las violencias colectivas que buscan responder a violencias previas en Argentina. De este modo, en primer lugar se presentará el concepto de acciones colectivas de violencia punitiva a partir de un breve repaso de nuestros trabajos previos. Desarrollaremos el uso que le hemos dado a la noción en investigaciones recientes, así como su relación con los trabajos acerca de los linchamientos y el fenómeno del vigilantismo en América Latina. La propuesta conceptual dialoga con dicha literatura, especificando un recorte en relación a las características del fenómeno empírico en el país. En este primer apartado se justificará también el abordaje metodológico. Posteriormente, presentaremos el análisis de los datos, describiendo el comportamiento de las acciones a lo largo del año. Se describirán las variaciones en relación a las distintas medidas gubernamentales adoptadas en distintos meses. Luego, analizaremos algunas características específicas de las acciones como el lugar en el que transcurren los hechos, los factores que precipitan los ataques y los objetos atacados en los mismos. Por último, en las conclusiones realizaremos un balance con las continuidades y cambios con respecto a los trabajos previos.Fil: Gamallo, Leandro Anibal. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Sociales. Instituto de Investigaciones "Gino Germani"; ArgentinaFil: González, Leandro Ignacio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Mar del Plata; Argentin
A comparison of wave-based discontinuous Galerkin, ultra-weak and least-square methods for wave problems
No full textSeveral numerical methods using non-polynomial interpolation have been proposed for wave propagation problems at high frequencies. The common feature of these methods is that in each element, the solution is approximated by a set of local solutions. They can provide very accurate solutions with a much smaller number of degrees of freedom compared to polynomial interpolation. There are however significant differences in the way the matching conditions enforcing the continuity of the solution between elements can be formulated. The similarities and discrepancies between several non-polynomial numerical methods are discussed in the context of the Helmholtz equation. The present comparison is concerned with the ultra-weak variational formulation (UWVF), the least-squares method (LSM) and the discontinuous Galerkin method with numerical flux (DGM). An analysis in terms of Trefftz methods provides an interesting insight into the properties of these methods. Second, the UWVF and the LSM are reformulated in a similar fashion to that of the DGM. This offers a unified framework to understand the properties of several non-polynomial methods. Numerical results are also presented to put in perspective the relative accuracy of the methods. The numerical accuracies of the methods are compared with the interpolation errors of the wave bases
A comparison of two wave element methods for the Helmholtz problem
No full textIn comparison with low-order finite element methods (FEMs), the use of oscillatory basis functions has been shown to reduce the computational complexity associated with the numerical approximation of Helmholtz problems at high wave numbers. We compare two different wave element methods for the 2D Helmholtz problems. The methods chosen for this study are the partition of unity FEM (PUFEM) and the ultra-weak variational formulation (UWVF). In both methods, the local approximation of wave field is computed using a set of plane waves for constructing the basis functions. However, the methods are based on different variational formulations; the PUFEM basis also includes a polynomial component, whereas the UWVF basis consists purely of plane waves. As model problems we investigate propagating and evanescent wave modes in a duct with rigid walls and singular eigenmodes in an L-shaped domain. Results show a good performance of both methods for the modes in the duct, but only a satisfactory accuracy was obtained in the case of the singular field. On the other hand, both the methods can suffer from the ill-conditioning of the resulting matrix system
Finite element methods in local active control of sound
No full textThe active control of sound is analyzed in the framework of the mathematical theory of optimal control. After setting the problem in the frequency domain, we deal with the state equation, which is a Helmholtz partial differential equation. We show the existence of a unique solution and analyze a finite element approximation when the source term is a Dirac delta measure. Two optimization problems are successively considered. The first one concerns the choice of phases and amplitudes of the actuators to minimize the noise at the sensors' location. The second one consists of determining the optimal actuators' placement. Both problems are then numerically solved. Error estimates are settled and numerical results for some tests are reported
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