Modelling of Scalar Wave Propagation Problems in Heterogeneous Media by the Explicit Green's Approach Method

2nd International Conference on Mathematical Modeling in Physical Sciences 2013

物理学;数学

Loureiro, F.S.^1 ; Mansur, W.J.^2

Department of Computer Science, Federal University of Juiz de Fora, Brazil^1

Department of Civil Engineering, COPPE/Federal University of Rio de Janeiro, CP 68506, Rio de Janeiro, CEP 21945-970, RJ, Brazil^2

关键词: Central difference;    Heterogeneous media;    Initial-boundary value problems;    Numerical green's function;    Scalar wave equation;    Scalar wave propagation;    Time integration;    Time-integration scheme;   

Others  :  https://iopscience.iop.org/article/10.1088/1742-6596/490/1/012214/pdf
DOI  :  10.1088/1742-6596/490/1/012214

来源: IOP

【 摘 要 】

The Explicit Green's approach is an effective method for solving initial-boundary value problems in any kind of medium and geometry. This is due to the fact that numerical Green's functions are adopted instead of analytical ones, rendering a more general approach. When the Explicit Green's approach is applied to the scalar wave equation and Green's functions are computed by the finite element method (FEM) in conjunction with the central difference time integration scheme, unstable results are observed. To circumvent this drawback, the present paper discusses the application of a time substep procedure to the central difference time integration for the Green's functions computation. The substep procedure has the advantage of stabilizing the solution as well as increasing the accuracy order in the time domain from two to four. Numerical examples that demonstrate the accuracy and effectiveness of the proposed methodology are provided.