A rotated staggered grid finite-difference with the absorbing boundary condition of a perfectly matched layer

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.

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An optimal absorbing boundary condition for finite difference modeling of acoustic and elastic wave propagation

The Journal of the Acoustical Society of America ◽

10.1121/1.408384 ◽

1994 ◽

Vol 95 (2) ◽

pp. 733-745 ◽

Cited By ~ 22

Author(s):

Chengbin Peng ◽

M. Nafi Toksöz

Keyword(s):

Boundary Condition ◽

Wave Propagation ◽

Finite Difference ◽

Elastic Wave ◽

Elastic Wave Propagation ◽

Absorbing Boundary Condition ◽

Absorbing Boundary

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Absorbing boundary condition for the elastic wave equation

Geophysics ◽

10.1190/1.1442496 ◽

1988 ◽

Vol 53 (5) ◽

pp. 611-624 ◽

Cited By ~ 47

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.

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