A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems, Based on Local Hermitian Interpolation with Radial Basis Functions

David Stevens; Henry Power; Michael Lees; Herve Morvan

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A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems, Based on Local Hermitian Interpolation with Radial Basis Functions

机译：基于带径向基函数的局部Hermitian插值的3D不饱和区问题的无网格求解技术

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摘要

Recent developments in meshless numerical methods have led to algorithms that can be used to solve arbitrarily large problems without the support of a connected mesh, and without the computational cost and numerical ill-conditioning issues usually associated with such solution techniques. This work applies the Local Hermitian Interpolation (LHI) method, based on local interpolation with Radial Basis Functions (RBFs), to the solution of 3D unsaturated porous media problems. The proposed implementation is capable of handling real soil properties, provided either as an analytical function or as a series of pointwise measurements. The technique is implemented with implicit and explicit timestepping, and is validated against two transient Richards' equation models, of which one has a known analytical solution. In addition, a real-world infiltration problem based on a saturated-unsaturated formulation is modelled, using a realistic variation of soil properties with water-pressure.

机译：无网格数值方法的最新发展导致了可用于解决任意大问题的算法，而无需连接网格的支持，也没有通常与此类解决方案技术相关的计算成本和数值不适问题。这项工作基于具有径向基函数（RBF）的局部插值，将局部Hermitian插值（LHI）方法应用于3D不饱和多孔介质问题的解决方案。所提出的实现方式能够处理真实的土壤特性，可以作为分析函数或一系列逐点测量来提供。该技术采用隐式和显式时间步长实施，并针对两个瞬态Richards方程模型进行了验证，其中一个模型具有已知的解析解。另外，利用土壤压力随水力的实际变化，模拟了基于饱和-不饱和配方的真实渗透问题。

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《Transport in Porous Media》 |2009年第2期|149-169|共21页
作者
David Stevens; Henry Power; Michael Lees; Herve Morvan;
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作者单位

School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham, UK;

School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham, UK;

School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham, UK;

School of Mechanical, Materials and Manufacturing Engineering, University of Nottingham, Nottingham, UK;

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正文语种 eng
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meshless collocation approach; local interpolation; radial basis functions; richard's equation; saturated-unsaturated flow;

机译：无网格搭配方法;局部插值径向基函数;理查德方程饱和-不饱和流;

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A Meshless Solution Technique for the Solution of 3D Unsaturated Zone Problems, Based on Local Hermitian Interpolation with Radial Basis Functions

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