Convolution Approximating Perfect Matched Layer Absorbing Boundary Condition of 3D Scalar Acoustic Wave Equation

2014 ◽  
Vol 971-973 ◽  
pp. 1095-1098
Author(s):  
Cong Wang ◽  
Jian Xun Zhang
Keyword(s):  
Differential Equation ◽  
Boundary Condition ◽  
Wave Equation ◽  
Order Differential Equation ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Equation ◽  
Third Order ◽  
Absorbing Boundary ◽  
Perfect Matched Layer

Because traditional displacement form of 3D acoustic perfectly matched layer (PML) absorbing condition needs to split the displacement into three parts, which requires solving a third-order differential equation in time and occupies a large amount of memory. In order to solve the above problems, this paper puts forward an Convolution approximating PML absorbing boundary condition based on the previous works, and discusses the basic construction of the traditional perfectly matched layer absorbing boundary condition and the new arithmetic in detail, then the new method is compared with absorbing condition of low order paraxial approximation and traditional PML, investigating the absorbing effects of 3D acoustic wave’s numerical records.

An Absorbing Boundary Condition Based on Perfectly Matched Layer Technique Combined with Discontinuous Galerkin Boltzmann Method for Low Mach Number Flow Noise

2018 ◽  
Vol 26 (04) ◽  
pp. 1850011 ◽  
Author(s):  
Weidong Shao ◽  
Jun Li
Keyword(s):  
Boundary Condition ◽  
Discontinuous Galerkin ◽  
Perfectly Matched Layer ◽  
Absorbing Boundary Condition ◽  
Time Behavior ◽  
Computational Domain ◽  
Mean Flow ◽  
Absorbing Boundary ◽  
Flow Noise ◽  
Boltzmann Method

For flow noise simulations, the nonreflecting boundary condition (NRBC) is significant to confine the computational domain to a small domain. Lattice Boltzmann method (LBM) has advantages for noise because of its low dissipation, but is limited to the uniform grid. In this paper, an absorbing boundary condition (ABC) based on perfectly matched layer (PML) technique is introduced to LBM. Then PML stability is analyzed and a new strategy is developed to achieve robustness. Invoking the decoupling time integration, the underlying equation for streaming is solved with the nodal discontinuous Galerkin method. Benchmark acoustic problems were used to demonstrate the PML absorption. Moreover, PML parameters, long time behavior and inhomogeneous pseudo mean flow are discussed. The methodology appears to work very well and would be hoped for practical flow noise computation.

scholarly journals Micro-Differential Boundary Conditions Modelling the Absorption of Acoustic Waves by 2D Arbitrarily-Shaped Convex Surfaces

2012 ◽  
Vol 11 (2) ◽  
pp. 674-690 ◽  
Author(s):  
Hélène Barucq ◽  
Julien Diaz ◽  
Véronique Duprat
Keyword(s):  
Wave Equation ◽  
Acoustic Waves ◽  
Principal Symbol ◽  
Absorbing Boundary Condition ◽  
Acoustic Wave Equation ◽  
Absorbing Boundary ◽  
Computational Burden ◽  
First Order ◽  
Robin Condition ◽  
Elliptic Regions

AbstractWe propose a new Absorbing Boundary Condition (ABC) for the acoustic wave equation which is derived from a micro-local diagonalization process formerly defined by M.E. Taylor and which does not depend on the geometry of the surface bearing the ABC. By considering the principal symbol of the wave equation both in the hyperbolic and the elliptic regions, we show that a second-order ABC can be constructed as the combination of an existing first-order ABC and a Fourier-Robin condition. We compare the new ABC with other ABCs and we show that it performs well in simple configurations and that it improves the accuracy of the numerical solution without increasing the computational burden.

Absorbing boundary condition for the elastic wave equation

Geophysics ◽  
1988 ◽  
Vol 53 (5) ◽  
pp. 611-624 ◽  
Author(s):  
C. J. Randall
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Finite Difference ◽  
Elastic Wave ◽  
Grazing Incidence ◽  
Scalar Fields ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary Condition ◽  
Elastic Wave Equation ◽  
Absorbing Boundary

Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.

A new absorbing boundary condition for diffusive‐viscous wave equation

2011 ◽  
Author(s):  
Haixia Zhao ◽  
Jinghuai Gao ◽  
Yichen Ma ◽  
Bin Weng ◽  
Zhenjiang Hao
Keyword(s):  
Boundary Condition ◽  
Wave Equation ◽  
Absorbing Boundary Condition ◽  
Absorbing Boundary
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