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An improved time-dependent Boundary Element Method for two-dimensional acoustic problems in a subsonic uniform flow

机译:亚音速均匀流中二维声学问题的一种改进的时变边界元方法

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In this paper, we have developed an improved formulation of two-dimensional Convected Boundary Element Method (CBEM) for radiation and propagation acoustic problems in a uniform mean flow with arbitrary orientation. The improved CBEM approach is derived from an advanced form of time-space two-dimensional Boundary Integral Equation (BIE) according to new Sommerfeld Radiation Conditions (SRC) with arbitrary mean flow. The acoustic variables of these formulations are expressed only in terms of the acoustic field as well as its normal and tangential derivatives. The multiplication operators are based explicitly on the two-dimensional Green's function and its convected normal derivative kernel. The proposed terms significantly reduce the presence of flow quantities incorporated in the classical integral formulations. Precisely, the convected kernel only requires the evaluation of two terms instead of several terms in conventional formulations due to the flow effects in the temporal and spatial derivatives. Also, for the singular integrations, the kernels containing logarithmic and weak singularities are converted to regular forms and evaluated partially analytically and numerically. The formulation is derived to be easy to implement as a numerical tool for computational codes of acoustic mediums with arbitrary mean flow. The accuracy and robustness of this technique is assessed through several examples such as the two-dimensional monopole, dipole and quadrupole sources in a uniform mean flow. An application of the improved formulation coupled with Particular Dirichlet-to-Neumann operators (PDtN) has been presented to describe the acoustic field inside two-dimensional infinite ducts in a uniform mean flow. The numerical results are compared to analytical, conventional BEM and Finite Element Method (FEM) formulations. (C) 2017 Elsevier B.V. All rights reserved.
机译:在本文中,我们已经开发了二维对流边界元方法(CBEM)的改进公式,该方法适用于在任意取向的均匀平均流中的辐射和传播声学问题。改进的CBEM方法是根据具有任意平均流的新Sommerfeld辐射条件(SRC)从高级形式的时空二维边界积分方程(BIE)派生而来的。这些公式的声学变量仅以声场及其法向和切向导数表示。乘法运算符明确地基于二维格林函数及其对流的正态导数核。拟议的条款大大减少了经典积分公式中包含的流量。精确地讲,由于时间和空间导数中的流动效应,对流核仅需要评估两个项,而不需要常规公式中的几个项。同样,对于奇异积分,包含对数和弱奇异性的内核将转换为规则形式,并通过分析和数字方式进行部分评估。该公式被推导为易于实现为具有任意平均流量的声介质计算代码的数值工具。该技术的准确性和鲁棒性通过几个示例进行了评估,例如均流中的二维单极,偶极和四极源。提出了一种改进的公式与特殊Dirichlet-to-Neumann算子(PDtN)结合的应用,以描述二维无限大导管内均匀均流中的声场。将数值结果与常规BEM和有限元方法(FEM)的分析公式进行比较。 (C)2017 Elsevier B.V.保留所有权利。

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