1,721,008 research outputs found
A comparison of solution approaches for the two-domain model of non equilibrium transport in porous media
No full textImpact of grid resolution on the integrated and distributed response of a coupled surface-subsurface hydrological model for the des Anglais catchment, Quebec
No full textDigital elevation models (DEMs) at different resolutions (180, 360, and 720 m) are used to examine the impact of different levels of landscape representation on the hydrological response of a 690-km2 catchment in southern Quebec. Frequency distributions of local slope, plan curvature, and drainage area are calculated for each grid size resolution. This landscape analysis reveals that DEM grid size significantly affects computed topographic attributes, which in turn explains some of the differences in the hydrological simulations. The simulations that are then carried out, using a coupled, process-based model of surface and subsurface flow, examine the effects of grid size on both the integrated response of the catchment (discharge at the main outlet and at two internal points) and the distributed response (water table depth, surface saturation, and soil water storage). The results indicate that discharge volumes increase as the DEM is coarsened, and that coarser DEMs are also wetter overall in terms of water table depth and soil water storage. The reasons for these trends include an increase in the total drainage area of the catchment for larger DEM cell sizes, due to aggregation effects at the boundary cells of the catchment, and to a decrease in local slope and plan curvature variations, which in turn limits the capacity of the watershed to transmit water downslope and laterally. The results obtained also show that grid resolution effects are less pronounced during dry periods when soil moisture dynamics are mostly controlled by vertical fluxes of evaporation and percolation
Assessment of Catchment-Scale Evapotranspiration in a Process-Based Integrated Model Via Boundary Condition Switching Vs Root Water Uptake Modeling
No full textPicard and Newton Linearization For the Coupled Model of Saltwater Intrusion In Aquifers
No full textDifficulties in the numerical solution of the partial differential equations governing seawater intrusion in aquifers arise from the coupling between the flow and transport equations and from the nonlinear aspects of this coupling. Several linearization approaches are discussed for the solution of the nonlinear system which results from a finite element discretization of the coupled equations. It is first shown that the most commonly used solution method can be viewed as a Picard linearization applied to the transport equation, with the coupling resolved by iteration over the two governing equations. The full Newton scheme for solving the coupled problem produces a Jacobian of size 2N x 2N, where N is the number of nodes in the discretization of both the flow and transport equations. To reduce the size and complexity of the full Newton scheme, a partial Newton method is proposed, which, like the Picard approach, produces matrix systems of size N x N. This scheme applies Newton linearization to the transport equation, and conventional iteration to resolve the coupling. Results from two- and three-dimensional test simulations show that the partial Newton scheme gives improved convergence and robustness compared to Picard linearization, especially for highly advective problems or large density ratios. Both approaches involve the solution of a symmetric (flow) and a nonsymmetric (transport) system of equations, and it is shown that the per iteration CPU cost for the partial Newton method is not significantly greater than that of the Picard scheme
Comment on "A combined Laplace transform and streamline upwind approach for nonideal transport of solutes in porous media
No full textA Comparison of Picard and Newton Iteration In the Numerical-solution of Multidimensional Variably Saturated Flow Problems
Full text linkPicard iteration is a widely used procedure for solving the nonlinear equation governing flow in variably saturated porous media. The method is simple to code and computationally cheap, but has been known to fail or converge slowly. The Newton method is more complex and expensive (on a per-iteration basis) than Picard, and as such has not received very much attention. Its robustness and higher rate of convergence, however, make it an attractive alternative to the Picard method, particularly for strongly nonlinear problems. In this paper the Picard and Newton schemes are implemented and compared in one-, two-, and three-dimensional finite element simulations involving both steady state and transient flow. The eight test cases presented highlight different aspects of the performance of the two iterative methods and the different factors that can affect their convergence and efficiency, including problem size, spatial and temporal discretization, initial solution estimates, convergence error norm, mass lumping, time weighting, conductivity and moisture content characteristics, boundary;conditions, seepage fades, and the extent of fully saturated zones in the soil. Previous strategies for enhancing the performance of the Picard and Newton schemes are revisited, and new ones are suggested. The strategies include chord slope approximations for the derivatives of the characteristic equations, relaxing convergence requirements along seepage faces, dynamic time step control, nonlinear relaxation, and a mixed Picard-Newton approach. The tests show that the Picard or relaxed Picard schemes are often adequate for solving Richards' equation, but that in cases where these fail to converge or converge slowly, the Newton method should be used. The mixed Picard-Newton approach can effectively overcome the Newton scheme's sensitivity to initial solution estimates, while comparatively poor performance is reported for the various chord slope approximations. Finally,given the reliability and efficiency of current conjugate gradient-like methods for solving linear nonsymmetric systems; the only real drawback of using Newton rather than Picard iteration is the algebraic complexity and computational cost of assembling the derivative terms of the Jacobian matrix, and it is suggested that both methods can be effectively implemented and used in numerical models of Richards' equation
Comparison between boundary condition switching and root water uptake modeling for assessment of catchment-scale evapotranspiration
Full text linkInfluence of spatial resolution on the distributed surface routing response of the des Anglais river basin (Canada)
No full textDigital elevation models (DEMs) at different resolutions (180, 360, and 720
m) are used to examine the impact of different levels of landscape representation on the
hydrological response of the des Anglais river basin (Canada). Frequency distributions
of local slope, plan curvature, and drainage area are calculated for each grid size resolution. This landscape analysis reveals that DEM grid size significantly affects computed
topographic attributes which in turn explain some of the differences in the hydrological
simulations. The investigation is carried out by analyzing the main hydrograph features
(peak flow, time to peak, and total volume) at the main outlet of the catchment over-3-
year simulation period. The simulation results, generated with the surface routing module
of a coupled surface–subsurface model, indicate that time to peak decreases as grid resolution is coarsened due to a decrease in flow path lengths, that peak flows increase as
grid resolution is refined due to an increase in local slopes, and that the simulated runoff
volumes increase at coarser grid resolution due to the aggregation of cells at the border
of the catchment
Finite element modeling of the transport of reactive contaminants in variably saturated soils with LEA and non-LEA sorption
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