Unconditional Stability Of Second-order Adi Schemes Applied To Multi-dimensional Diffusion Equations With Mixed Derivative Terms

K.J. in t Hout; B.D. Welfert

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Unconditional Stability Of Second-order Adi Schemes Applied To Multi-dimensional Diffusion Equations With Mixed Derivative Terms

机译：具有混合导数项的多维扩散方程的二阶Adi格式的无条件稳定性

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We consider the unconditional stability of second-order ADI schemes in the numerical solution of finite difference discretizations of multi-dimensional diffusion problems containing mixed spatial-derivative terms. We investigate an ADI scheme proposed by Craig and Sneyd, an ADI scheme that is a modified version thereof, and an ADI scheme introduced by Hundsdorfer and Verwer. Both sufficient and necessary conditions are derived on the parameters of each of these schemes for unconditional stability in the presence of mixed derivative terms. Our main result is that, under a mild condition on its parameter H, the second-order Hundsdorfer and Verwer scheme is unconditionally stable when applied to semi-discretized diffusion problems with mixed derivative terms in arbitrary spatial dimensions k≥2.

机译：在包含混合空间导数项的多维扩散问题的有限差分离散化数值解中，我们考虑了二阶ADI方案的无条件稳定性。我们研究了Craig和Sneyd提出的ADI方案，这是其改进版本的ADI方案，以及Hundsdorfer和Verwer引入的ADI方案。在存在混合导数项的情况下，对于这些条件中的每一个的参数，都得出了充分条件和必要条件，以实现无条件的稳定性。我们的主要结果是，在温和的参数H条件下，当将二阶Hundsdorfer and Verwer方案应用于具有任意空间维数k≥2的混合导数项的半离散扩散问题时，它是无条件稳定的。

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来源
《Applied numerical mathematics》 |2009年第4期|677-692|共16页
作者
K.J. in t Hout; B.D. Welfert;
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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);
原文格式 PDF
正文语种 eng
中图分类
关键词
initial-boundary value problems; diffusion equations; numerical solution; finite difference methods; adi splitting schemes; von neumann stability analysis; fourier analysis;

机译：初边值问题;扩散方程;数值解;有限差分法;adi分裂方案;von neumann稳定性分析;傅立叶分析;

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专利

1. Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms [J] . K.J. int Hout, C. Mishra Applied numerical mathematics . 2013,第deca期

机译：带有混合导数项的多维扩散方程的ADI方案的稳定性
2. Stability interval for explicit difference schemes for multi-dimensional second-order hyperbolic equations with significant first-order space derivative terms [J] . Mohanty RK Applied mathematics and computation . 2007,第2期

机译：具有重要一阶空间导数项的多维二阶双曲方程显式差分格式的稳定性区间
3. A new stability result for the modified Craig-Sneyd scheme applied to two-dimensional convection-diffusion equations with mixed derivatives [J] . Mishra Chittaranjan Applied mathematics and computation . 2016,第Null期

机译：修正的Craig-Sneyd格式在带有混合导数的二维对流扩散方程中的新稳定性结果
4. High-Order ADI Schemes for Convection-Diffusion Equations with Mixed Derivative Terms [C] . B. Duering, M. Fournie, A. Rigal International conference on spectral and high order methods . 2014

机译：具有混合导数项的对流扩散方程的高阶ADI格式
5. Stability Analysis of Numerical Schemes for Convection-dominated Diffusion and Navier-Stokes Equations [D] . Deng, Yongzhe. 2017

机译：对流统治扩散和Navier-Stokes方程数值方案的稳定性分析
6. Approximate series solution of multi-dimensional time fractional-order (heat-like) diffusion equations using FRDTM [O] . Brajesh K. Singh, Vineet K. Srivastava 2015

机译：使用FRDTM的多维时间分数阶（类热）扩散方程的近似级数解
7. Stability of ADI schemes for multidimensional diffusion equations with mixed derivative terms [O] . Hout, Karel in 't, Mishra, Chittaranjan 2012

机译：具有时滞的多维扩散方程的aDI格式的稳定性混合衍生术语
8. Conservative, Unconditionally Stable, Second Order Three-Point Difference Scheme for the Diffusion-Convection Equation [R] . Clauser, C., Kiesner, S. 1986

机译：扩散 - 对流方程的保守，无条件稳定，二阶三点差分格式

Unconditional Stability Of Second-order Adi Schemes Applied To Multi-dimensional Diffusion Equations With Mixed Derivative Terms

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