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A Kind of Discrete non-reflecting boundary conditions for Varieties of Wave Equations

Acta Mathematicae Applicatae Sinica 2002年第2期18卷 295-308页

作者： Xiu-min Shao, Zhi-ling LanInstitute of Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences, Beijing 100080, China Institute of Mathematics Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing China

In this paper, a new kind of discrete non-reflecting boundary conditions is developed. It can be used for a variety of wave equations such as the acoustic wave equation, the isotropic and anisotropic elastic wave equations and the equations for wave propagation in multi-phase media and so on. In this kind of boundary conditions, the composition of all artificial reflected waves, but not the individual reflected ones, is considered and eliminated. Thus, it has a uniform formula for different wave equations. The velocity CA of the composed reflected wave is determined in the way to make the reflection coefficients minimal, the value of which depends on equations. In this paper, the construction of the boundary conditions is illustrated and CA is found, numerical results are presented to illustrate the effectiveness of the boundary conditions.

关键词： Wave equations non-reflecting boundary conditions

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Finite Volume Methods for Wave Propagation in Stratified Magneto-Atmospheres

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Communications in Computational Physics 2010年第3期7卷 473-509页

作者： Franz Georg Fuchs Andrew D.McMurry Siddhartha Mishra Nils Henrik Risebro Knut Waagan Centre of Mathematics for Applications(CMA) University of OsloP.O.Box 1053BlindernN-0316 OsloNorway High Altitude Observatory(HAO) National Center of Atmospheric ResearchP.O.Box 3000Boulder80307-3000 ColoradoUSA

We present a model for simulating wave propagation in stratified magnetoatmospheres. The model is based on equations of ideal MHD together with gravitational source terms. In addition, we present suitable boundary data and steady statesto model wave propagation. A finite volume framework is developed to simulate thewaves. The framework is based on HLL and Roe type approximate Riemann solversfor numerical fluxes, a positivity preserving fractional steps method for discretizingthe source and modified characteristic and Neumann type numerical boundary conditions. Second-order spatial and temporal accuracy is obtained by using an ENO piecewise linear reconstruction and a stability preserving Runge-Kutta method *** boundary closures are suitably modified to ensure mass balance. The numericalframework is tested on a variety of test problems both for hydrodynamic as well asmagnetohydrodynamic configurations. It is observed that only suitable choices of HLLsolvers for the numerical fluxes and balanced Neumann type boundary closures yieldstable results for numerical wave propagation in the presence of complex magneticfields.

关键词： Solar atmospheres MHD equations finite volume methods non-reflecting boundary conditions

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A Flexible boundary Procedure for Hyperbolic Problems: Multiple Penalty Terms Applied in a Domain

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Communications in Computational Physics 2014年第7期16卷 541-570页

作者： Jan Nordstrom Qaisar Abbas Brittany A.Erickson Hannes Frenander Department of Mathematics Division of Computational MathematicsLinkoping UniversitySE-58183 Link¨opingSweden Department of Information Technology Division of Scientific ComputingUppsala UniversitySE-75105 UppsalaSweden Department of Geological Sciences San Diego State UniversitySan DiegoCA 92182-1020USA Department of Mathematics Division of Computational MathematicsLinkoping UniversitySE-58183 Link¨opingSweden.

A new weak boundary procedure for hyperbolic problems is *** consider high order finite difference operators of summation-by-parts form with weak boundary conditions and generalize that *** new boundary procedure is applied near boundaries in an extended domain where data is *** show how to raise the order of accuracy of the scheme,how to modify the spectrum of the resulting operator and how to construct non-reflecting properties at the *** new boundary procedure is cheap,easy to implement and suitable for all numerical methods,not only finite difference methods,that employ weak boundary *** results that corroborate the analysis are presented.

关键词： Summation-by-parts weak boundary conditions penalty technique high-order accuracy finite difference schemes stability steady-state non-reflecting boundary conditions

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