A spectral element solution of the Klein-Gordon equation with high-order treatment of time and non-reflecting boundary

被引：17
作者：
Lindquist, Joseph M. [1 ]
Neta, Beny [1 ]
Giraldo, Francis X. [1 ]
机构：
[1] USN, Postgrad Sch, Dept Appl Math, Monterey, CA 93943 USA
来源：
WAVE MOTION | 2010年 / 47卷 / 05期
关键词：
Klein-Gordon equation; High-order; Non-reflecting boundary condition; Spectral elements; Higdon; Givoli-Neta; Runge-Kutta; DEPENDENT SCATTERING; DISPERSIVE WAVES; FORMULATION; EXTENSIONS; SCHEME;
D O I：
10.1016/j.wavemoti.2009.11.007
中图分类号：
O42 [声学];
学科分类号：
070206 ; 082403 ;
摘要：
A spectral element (SE) implementation of the Givoli-Neta non-reflecting boundary condition (NRBC) is considered for the solution of the Klein-Gordon equation. The infinite domain is truncated via an artificial boundary B, and a high-order NRBC is applied on B. Numerical examples, in various configurations, concerning the propagation of a pressure pulse are used to demonstrate the performance of the SE implementation. Effects of time integration techniques and long term results are discussed. Specifically, we show that in order to achieve the full benefits of high-order accuracy requires balancing all errors involved: this includes the order of accuracy of the spatial discretization method, time-integrators, and boundary conditions. Published by Elsevier B.V.
引用
收藏
页码：289 / 298
页数：10
相关论文
共 29 条
[1]   RADIATION BOUNDARY-CONDITIONS FOR WAVE-LIKE EQUATIONS [J].
BAYLISS, A ;
TURKEL, E .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1980, 33 (06) :707-725
[2]  
Collier T.K., 1993, Environmental Sciences, V2, P161
[3]  
CURTIS AR, 1975, J I MATH APPL, V16, P35
[4]   High-order non-reflecting boundary conditions for the linearized 2-D Euler equations: No mean flow case [J].
Dea, John R. ;
Giraldo, Francis X. ;
Neta, Beny .
WAVE MOTION, 2009, 46 (03) :210-220
[5]   A study of spectral element and discontinuous Galerkin methods for the Navier-Stokes equations in nonhydrostatic mesoscale atmospheric modeling: Equation sets and test cases [J].
Giraldo, F. X. ;
Restelli, M. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2008, 227 (08) :3849-3877
[6]   Recent advances in the DtN FE Method [J].
Givoli, D .
ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING, 1999, 6 (02) :71-116
[7]   High-order local non-reflecting boundary conditions: a review [J].
Givoli, D .
WAVE MOTION, 2004, 39 (04) :319-326
[8]   Finite element analysis of time-dependent semi-infinite wave-guides with high-order boundary treatment [J].
Givoli, D ;
Neta, B ;
Patlashenko, I .
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING, 2003, 58 (13) :1955-1983
[9]   High-order non-reflecting boundary conditions for dispersive waves [J].
Givoli, D ;
Neta, B .
WAVE MOTION, 2003, 37 (03) :257-271
[10]   High-order non-reflecting boundary scheme for time-dependent waves [J].
Givoli, D ;
Neta, B .
JOURNAL OF COMPUTATIONAL PHYSICS, 2003, 186 (01) :24-46
123