Dual Reciprocity Boundary Element Method untuk Menyelesaikan Masalah Infiltrasi Stasioner pada Saluran Datar Periodik

Abstrak. Penelitian ini membahas tentang penyelesaian masalah infiltrasi stasioner dari saluran datar dengan Dual Reciprocity Boundary Element Method (DRBEM). Persamaan pembangun untuk masalah ini adalah persamaan Richard. Menggunakan transformasi Kirchhoff dan relasi eksponensial konduktifitas hidrolik, persamaan Richard ditransformasi ke dalam persamaan infiltrasi stasioner dalam Matric Flux Potential (MFP). Persamaan infiltrasi dalam MFP selanjutnya diubah ke dalam persamaan Helmholtz termodifikasi. Model matematika infiltrasi stasioner pada saluran datar berbentuk Masalah Syarat batas Helmholtz termodifikasi Solusi numerik diperoleh dengan menyelesaikan persamaan Helmholtz termodifikasi menggunakan Dual Reciprocity Boundary Element Method (DRBEM) dengan pengambilan jumlah titik kolokasi eksterior dan interior yang bervariasi. Lebih lanjut, solusi numerik dan solusi analitik dibandingkan..Kata Kunci: Infiltrasi, saluran datar, persamaan helmholtz termodifikasi, DRBEM.Abstract. This research discusses about the problem solving of steady infiltration problem from flat channel with Dual Reciprocity Boundary Element Method (DRBEM). The governing equation for this problem is Richard’s equation. Using Kirchhoff transformation and exponential hydraulic conductivity relation, Richard’s equation is transformed into steady infiltration equation in the form of MFP. Infiltration equation in the form of MFP is then transformed to modified Helmholtz equation. A mathematical model of steady infiltration from flat channel in the form of boundary condition problem of modified Helmholtz EQUATION. Numerical solution is obtained by solving modified Helmholtz equation by using Dual Reciprocity Boundary Element Method (DRBEM) with various number of exterior and interior collocation points. Moreover, numerical and analytic solution are then compared.Keywords: infiltration, flat channel, modified Helmholtz equation, DRBEM

Morris method with improved sampling strategy and Sobol’ Variance-based method, as validation tool on Numerical Model of Richard’s Equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

Evaluating long-term potential evapotranspiration and soil moisture dynamics at Shanghai City China

As the finical hub of China, the Shanghai metropolitan area is one of the most important regions on earth, which requires significant efforts in water, energy and resources management and supply. Ongoing dynamic changes in climate have posed large uncertainties in our ability to better quantify, estimate and predict future hydrological and ecological responses, including soil moisture dynamics and potential evapotranspirative demands. Given these significant implications, in this study, we focused on better understanding long-term dynamic trends in soil moisture and potential evapotranspiration at Shanghai with the Hargreaves equation and 1-Dimensional flow transport with Richard’s equation. We further tested how perturbations in temperature and precipitation patterns influence soil moisture and potential evapotranspiration responses. Our results suggested significant correlation between temperature and potential evapotranspiration as well as precipitation inputs and soil moisture. We believe these results can provide useful insights to help us better understand the hydrological responses at Shanghai to climate change.

A Thermo-Hydro-Mechanical Coupling Analysis for the Contaminant Transport in a Bentonite Barrier with Variable Saturation

The migration of hazardous substances in a bentonite barrier layer is a key issue for the safety of nuclear waste storage. This study develops a thermo-hydro-mechanical coupling model to simulate the contaminant migration in a bentonite barrier layer of the nuclear waste storage chamber. In particular, the Richard’s equation is used to describe the groundwater flow in the bentonite barrier layer with variable saturation. Thermal diffusion and concentration diffusion are coupled with the layer deformation and fluid flow. The migration rate and diffusion range of hazardous substances in the bentonite barrier layer are numerically simulated. These numerical simulations show that the heat release from nuclear waste can induce a temperature gradient and deformation, and thus significantly affects both transfer rate and concentration distribution of dilute substances. These multi-physical couplings under different initial saturation may significantly modify the sealing efficiency of an unsaturated bentonite barrier layer and thus this model is of great significance in the safety evaluation of a nuclear waste disposal repository.

Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

An Accurate Inverse Model for the Detection of Leaks in Sealed Landfills

Leaks from landfills to underlying soil layers are one of the main problems that endanger the sustainability of waste disposal in landfills. Indeed, the possible failing of in-situ equipment can give rise to serious pollution consequences or costly inspection work in the landfill body. In this paper, we develop the time dependent mathematical relationship between the concentration of water at the surface of the landfill and the flux at the bottom of the landfill. This makes it possible to detect a leak using non-expensive measurements made at the surface of the landfill. The resulting model is obtained by analytically solving Richard’s equation with a piecewise linear boundary condition at the bottom. The unknown coefficients of the piecewise linear functions, which can be estimated using the measurements at the surface, provide the necessary information for detecting leaks. The algorithm has been numerically tested using simulated data of rain precipitation. The method proposed could be conveniently used to complement the usual monitoring techniques due to the limited costs of its implementation.

Analysis Infiltration Waters in Various Forms of Irrigation Channels by Using Dual Reciprocity Boundary Element Method

This research discusses the infiltration of furrow irrigation invarious forms of irrigation channels in homogeneous soils. The governing equation of the problems is a Richard’s Equation. This equation is transformed using a set of transformation including Kirchhoff and dimensionless variables into Helmholtz modified equations. Furthermore with Dual Reciprocity Boundary Element Method (DRBEM), numerical solution of modified Helmholtz equation obtained. The proposed method is tested on problem involved infiltration from periodic flat channels, non-flat channels without impermeable and non-flat channels with impermeable. The greatest value of suction potential and water content is located below the channel surface. The most water consecutively is a non-flat channel without impermeable, non-flat channel with impermeable and flat channel on Lakish Clay soils.

Application of the Surface Energy Balance in Richard's equation-based model using climatic data to calculate soil evaporation

<p>This research aims to observe the behaviour between heat flow at the limit of the unsaturated area and the earth's surface (evaporation) through different methods based on the surface energy balance. This behavior has been determined by the DRUtES. DRUtES is a free software able to determine the evaporation in the surface using climate and hydraulic parameters determined by the Richard equation. Richards’ equation describes the flow of water in an unsaturated porous medium due to the actions of gravity and capillarity neglecting the flow of the non-wetting phase, usually air (Farthing & Ogden, 2017). </p><p> </p><p>The results obtained have been compared with the Penman-Monteith potential evapotranspiration model, this one as a referenced value. The results obtained help to understand the loss of water in the unsaturated area. This first approach using DRUtES and evaporation methods will allow a deeper investigation in the future regarding the impact of climate change on climate variables and their effects on soil moisture (unsaturated area) and natural aquifer recharge.</p><p><strong>Key words</strong>: Evaporation, surface energy balance, Richard's Equation, zone unsaturated, Penman-Monteith.</p>

Morris method with improved sampling strategy and Sobol’ variance-based method, as validation tool on numerical model of Richard’s equation

Richard’s equation was approximated by finite-difference numerical scheme to model water infiltration profile in variably unsaturated soil. The published data of Philip’s semi-analytical solution was used to validate the simulated results from the numerical scheme. A discrepancy was found between the simulated and the published semi-analytical results. Morris method as a global sensitivity tool was used as an alternative to local sensitivity analysis to assess the results discrepancy. Morris method with different sampling strategies were tested, of which Manhattan distance method have resulted a better sensitivity measures and also a better scan of input space than Euclidean method. Moreover, Morris method at and Manhattan distance sampling strategy, with only 2 extra simulation runs than local sensitivity analysis, was able to produce reliable sensitivity measures ( , ). The sensitivity analysis results were cross-validated by Sobol’ variance-based method with 150,000 simulation runs. The global sensitivity tool has identified three important parameters, of which spatial discretization size was the sole reason of the discrepancy observed. In addition, a high proportion of total output variance contributed by parameters and is suggesting a greater significant digits is required to reduce its input uncertainty range.

Numerical Simulation of Unsaturated Soil Water from a Trickle Irrigation System for Sandy Loam Soils

Trickle irrigation is a system for supplying filtered water and fertilizer directly into the soil and water and it is allowed to dissipate under low pressure in an exact predetermined pattern. An equation to estimate the wetted area of unsaturated soil with water uptake by roots is simulated numerically using the HYDRUS-2D/3D software. In this paper, two soil types, which were different in saturated hydraulic conductivity were used with two types of crops tomato and corn, different values of emitter discharge and initial volumetric soil moisture content were assumed. It was assumed that the water uptake by roots was presented as a continuous sink function and it was introduced into Richard's equation in the unsaturated zone. Equations for wetted depth and radius were predicted. A good agreement was found between the predicted results with those obtained from the experiment field work. The maximum error of the predicted results were 23%, and 0.98 for modeling efficiency (EF), moreover, the root square error (RMSE) was below 0.95 cm.