scholarly journals Effect of hysteresis on water flow in the vadose zone under natural boundary conditions, Siloam Village case study, South Africa

2017 ◽  
Vol 20 (1) ◽  
pp. 88-99 ◽  
Author(s):  
I. A. Arrey ◽  
J. O. Odiyo ◽  
R. Makungo ◽  
M. O. Kataka
Keyword(s):  
Boundary Conditions ◽  
Vadose Zone ◽  
Zone Model ◽  
Natural Boundary ◽  
One Dimensional ◽  
Equation Analysis ◽  
Richard's Equation ◽  
1D Model ◽  
Natural Boundary Conditions ◽  
Hydrus 1D

Abstract A one-dimensional vadose zone model was used to simulate flow under natural boundary conditions. The effects of hysteresis and temporal variability of meteorological conditions were evaluated. Simulations were performed in HYDRUS-1D code for the period April 2013–January 2014 (6601 hours) at three different locations in a delineated portion of the sub-quaternary catchment A80A of Nzhelele with different soil textures. Soil hydraulic characteristics were estimated in a Rosetta library dynamically linked to the HYDRUS-1D model which is based on the numerical solution of a one-dimensional Richard's equation. Analysis of the simulation results suggests that ignoring hysteresis for soils of similar textural class does not lead to any significant deviation of the model predicted soil moisture, unlike for soils with different textural classes.

scholarly journals Elements of Bi-cubic Polynomial Natural Spline Interpolation for Scattered Data: Boundary Conditions Meet Partition of Unity Technique

2020 ◽  
Vol 8 (4) ◽  
pp. 994-1010
Author(s):  
Weizhi Xu
Keyword(s):  
Boundary Conditions ◽  
Spline Interpolation ◽  
Partition Of Unity ◽  
Scattered Data ◽  
Rectangular Domain ◽  
Natural Boundary ◽  
Natural Spline ◽  
Cubic Polynomial ◽  
Natural Boundary Conditions ◽  
Cubic Polynomials

This paper investigates one kind of interpolation for scattered data by bi-cubic polynomial natural spline, in which the integral of square of partial derivative of two orders to x and to y for the interpolating function is minimal (with natural boundary conditions). Firstly, bi-cubic polynomial natural spline interpolations with four kinds of boundary conditions are studied. By the spline function methods of Hilbert space, their solutions are constructed as the sum of bi-linear polynomials and piecewise bi-cubic polynomials. Some properties of the solutions are also studied. In fact, bi-cubic natural spline interpolation on a rectangular domain is a generalization of the cubic natural spline interpolation on an interval. Secondly, based on bi-cubic polynomial natural spline interpolations of four kinds of boundary conditions, and using partition of unity technique, a Partition of Unity Interpolation Element Method (PUIEM) for fitting scattered data is proposed. Numerical experiments show that the PUIEM is adaptive and outperforms state-of-the-art competitions, such as the thin plate spline interpolation and the bi-cubic polynomial natural spline interpolations for scattered data.

Meshless Integral Method for Analysis of Elastoplastic Geotechnical Materials

2010 ◽  
Author(s):  
Jianfeng Ma ◽  
Joshua David Summers ◽  
Paul F. Joseph
Keyword(s):  
Boundary Conditions ◽  
Function Approximation ◽  
Integral Method ◽  
Weak Form ◽  
Constitutive Law ◽  
Governing Equations ◽  
Natural Boundary ◽  
Pressure Sensitive ◽  
Support Domain ◽  
Natural Boundary Conditions

The meshless integral method based on regularized boundary equation [1][2] is extended to analyze elastoplastic geotechnical materials. In this formulation, the problem domain is clouded with a node set using automatic node generation. The sub-domain and the support domain related to each node are also generated automatically using algorithms developed for this purpose. The governing integral equation is obtained from the weak form of elastoplasticity over a local sub-domain and the moving least-squares approximation is employed for meshless function approximation. The geotechnical materials are described by pressure-sensitive multi-surface Drucker-Prager/Cap plasticity constitutive law with hardening. A generalized collocation method is used to impose the essential boundary conditions and natural boundary conditions are incorporated in the system governing equations. A comparison of the meshless results with the FEM results shows that the meshless integral method is accurate and robust enough to solve geotechnical materials.

On natural boundary conditions and DQM

1998 ◽  
Vol 25 (3) ◽  
pp. 279-286 ◽  
Author(s):  
M.A. De Rosa ◽  
C. Franciosi
Keyword(s):  
Boundary Conditions ◽  
Natural Boundary ◽  
Natural Boundary Conditions
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