M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated ow equation, Water Resour. Res. 26 (1990), 1483-1496.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... Soil moisture movement is assumed to obey classical Richards equation in studying the unsaturated zone [Hillel, 1980] Although the q based Richards equation degenerates in fully saturated media, and material heterogeneity produces discontinuous q profiles in solving groundwater hydrology problems [Celia et al. 1990], most land surface models also use it to capture the diurnal, seasonal, and annual variations in soil moisture because of their practical applications and various updatings. The updatings, such as in NCAR LSM (1.0) can prevent soil layers from becoming too wet, and also most land surface models ....

....are designed to function at coarse spatial resolution and large time steps. NCAR LSM uses six layers for the entire soil column of depth of 6.3 meters. The solution of the differential equation (5) however, is best approximated by integration over a fine spatial grid and small time step (e.g. Celia et al. 1990). Therefore, a set of experiments with very fine space and time steps were designed. The soil was divided into 630 1 cm layers and a 1 second time step was used. Initial soil moisture and boundary conditions were taken as case 3 discussed previously. The relative differences of the EWFAI [e.g. ....

CELIA, M.A., F.T. BOULOUTAS, and R.L. ZARBA, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26(7), 1483-1496, 1990.

....[33] to construct a coarse mesh for two level Schwarz methods. Our coarse mesh differs from other constructions, for example that in [9] in that no coarse mesh geometry need be created, and we do not need geometric information about the subdomains. The mixed form of Richards Equation is [8] S S S### # t # S ### t =r##K S k r# ##r## z## W (1.1) where # is pressure head; S S is the specific storage, which accounts for water compressibility and aquifer elasticity; S ### is the water saturation or volumetric fraction of pore space occupied by water; # is the porosity or ....

M.A.CELIA,E.T.BOULOUTAS, AND R. L. ZARBA, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26 (1990), pp. 1483--1496.

....[33] to construct a coarse mesh for two level Schwarz methods. Our coarse mesh differs from other constructions, for example that in [9] in that no coarse mesh geometry need be created, and we do not need geometric information about the subdomains. The mixed form of Richards Equation is [8] S S S( t j S ( t = r Delta [K S k r ( r ( z) W (1.1) where is pressure head; S S is the specific storage, which accounts for water compressibility and aquifer elasticity; S ( is the water saturation or volumetric fraction of pore space occupied by water; j is the ....

M. A. CELIA, E. T. BOULOUTAS, AND R. L. ZARBA, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26 (1990), pp. 1483--1496.

....equation is commonly used in modeling the flow of water in the unsaturated zone. It is obtained by combining Darcy s law with the continuity equation. We write Richard s equation using pressure head = p=fl, where p is pressure and fl is the specific weight of the fluid, as primary variable [1]. The water flux q in variably saturated porous media is governed by the extended form of Darcy s law [2, 3] q = GammaK r ( K s r ( z) 1) where K r ( is the relative hydraulic conductivity, K s is the saturated hydraulic conductivity tensor, r is the gradient operator, and z is ....

M. A. Celia, E. T. Boutoulas, and R. L. Zarba. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resour. Res., 26(7):1483--1496, 1990.

....in some added expense. Spline issues are discussed in more detail below. 4.2. Nonlinear Solution Methods To find an approximating solution fp i ; 1 i n n g to (7) requires solving a system of nonlinear equations. For the purpose of this work, we use either modified Picard iteration (MPI) [Celia et al. 1990] or full Newton iteration (NI) The MPI technique produces a simple computational algorithm that is mass conserving for numerical approximations that preserve spatial symmetry. The NI system is formed from (7) by defining f i = 1 Deltat 2 4 l 1 i Gamma l i S s S a p l 1 i ....

....the transformation approaches for solving RE to traditional solution methods using eight sets of test conditions, which are summarized in Tables 2 and 3. Tables 2 and 3 Four of these conditions (Problems A D) have been used previously in the literature as test problems [Miller and Kelley, 1994] [Celia et al. 1990; Rathfelder and Abriola, 1994] Forsyth et al. 1995] Problems E H represent various soil textural groups sand, loamy sand, loam, and clay loam, respectively, according to the USDA classification [Soil Conservation Service, 1975] as estimated by Carsel and Parrish [Carsel and Parrish, 1988] ....

Celia, M. A., E. T. Bouloutas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Wat. Resour. Res., 26(7), 1483-1496, 1990.

....related to the mean pore size, n v is a parameter related to the uniformity of the pore size distribution, and K s is the water saturated hydraulic conductivity. 2. 2 Spatial Discretization We use a standard finite difference approximation to discretize RE with respect to the spatial dimension [Celia et al. 1990)Celia, Bouloutas, and Zarba, z, where z 2 [0; Z] We consider a uniform spatial discretization comprised of n n Gamma 1 intervals f[z i ; z i 1 ]g nn Gamma1 i=1 , of length Deltaz, with Deltaz = Z= n n Gamma 1) and z i = i Gamma 1) Deltaz for 1 i n n . The spatial operator O sd ( ....

Celia, M. A., E. T. Bouloutas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Wat. Resour. Res., 26(7), 1483--1496, 1990.

....based on the local least squares functional allow the resolution of the steep saturation fronts which occur as water infiltrates dry soil. Such techniques are needed in order to avoid spurious oscillations in the finite element approximation (for details on this issue and other remedies see, e.g. [11] and [14] The following section presents the necessary background on the least squares formulation of the system arising in variably saturated subsurface flow. The finite element approximation properties for the first order system least squares formulation of the elliptic boundary value problems ....

M. A. Celia, E. T. Bouloutas, and R. L. Zarba. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resources Research, 26:1483--1496, 1990.

....satisfy the so called divergence free property. In Finite Element (FE) simulations, velocities are generally calculated by differentiation of the head solution. This approach may lead to violation of the mass conservation principle, and thus to inherently inaccurate contaminant fate predictions [4]. This behavior may be attributed to the fact that the discrete normal fluxes are discontinuous across element boundaries and hence local mass conservation is not warranted [29] One way to overcome this problem is to properly exploit the local subdomains where the mass conservation property of ....

.... to write Richard s equation in a number of different forms, depending on whether pressure head = p=fl, where p is pressure and fl is the specific weight of the fluid, or moisture content = nSw , where n is the porosity of the medium and Sw is the water saturation, are used as primary variables [4, . For practical purposes, it is convenient to use a pressure head formulation so that the simultaneous simulation of both fully saturated (Sw = 1) and unsaturated (Sw 1) conditions is possible [18, The water flux q is governed by the extended form of Darcy s law [25, 1, q = GammaK s K ....

M. A. Celia, E. T. Boutoulas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26 (1990), pp. 1483--1496.

....13 3.7 The Re1 problem The formulation described in (2.18) is termed a mixed form Richard s equation (MFRE) since both and appear as dependent variables. In our context, we expand the term around the iteration level, m, in terms of , followed by solution using Picard iteration [10]. By the truncated Taylor series approximation, we have p 1;m 1 k = p 1;m k ( p 1;m 1 k Gamma p 1;m k ) k fi fi fi fi p 1;m for k = 1; N; 3.4) where N is the number of nodes in the system. The initial boundary value problem is solved using the finite element method ....

M. A. Celia and E. T. Bouloutas. A general mass-conservative numerical solution for the unsaturated flow equation, Water Resources Research, 26(7):1483--1496, 1990.

.... Gamma10 . 3.6 The Re1 problem The formulation described in (2.16) is termed a mixed form Richard s equation (MFRE) since both and appear as dependent variables. In our context, we expand the term around the iteration level, m, in terms of , followed by solution using Picard iteration [9]. By the truncated Taylor series approximation, we have p 1;m 1 k = p 1;m k ( p 1;m 1 k Gamma p 1;m k ) k fi fi fi fi p 1;m for k = 1; N; 3.3) where N is the number of nodes in the system. The initial boundary value problem is solved using the finite element method ....

M. A. Celia and E. T. Bouloutas. A general mass-conservative numerical solution for the unsaturated flow equation. Water Resources Research, 26(7):1483--1496, 1990.

....is needed to support the flow of a gas phase compared to the pressure gradient needed to support an equal volumetric flow of an aqueous phase. Constitutive relations are required to close the conservation law; we detail this formulation below. The pressure head form of RE in one space dimension is [6] [c( S s S a ( t = z K( z 1 (1.1) where is pressure head; c( is the specific moisture capacity; is the volumetric fraction of the water phase; S s is the specific storage, which accounts for the slight compressibility of water; S a ( n ....

M. A. Celia, E. T. Bouloutas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow problem, Water Resources Research, 7 (1990), pp. 1483-- 1496.

....approximation approaches the most common way of solving RE. Many reports of approximate numerical solutions to RE have appeared in the literature, with low order finite difference [Hanks and Bowers, 1962; Rubin, 1968; Hornberger and Remson, 1969; Cooley, 1971; Freeze, 1971; Vauclin et al. 1979; Celia et al. 1990] and finite element [Cooley, 1983; Huyakorn et al. 1984; Allen and Murphy, 1986; Celia et al. 1990] the most common methods. Such solutions to RE are used routinely for applications involving agricultural, geochemical, and nuclear waste disposal applications [van der Heidje, 1996] among others. ....

.... to RE have appeared in the literature, with low order finite difference [Hanks and Bowers, 1962; Rubin, 1968; Hornberger and Remson, 1969; Cooley, 1971; Freeze, 1971; Vauclin et al. 1979; Celia et al. 1990] and finite element [Cooley, 1983; Huyakorn et al. 1984; Allen and Murphy, 1986; Celia et al. 1990] the most common methods. Such solutions to RE are used routinely for applications involving agricultural, geochemical, and nuclear waste disposal applications [van der Heidje, 1996] among others. The robust solution of these applications is desirable, but is not currently possible for certain ....

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Celia, M. A., E. T. Bouloutas, and R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Wat. Resour. Res., 26,(7), 1483-1496, 1990.

....under the U.S. Department of Energy s Partnership in Computational Science Program is a saturatedunsaturated finite element flow code coupled with an upstream weighted finite element transport solver. In this particular implementation we have used the mixed formulation of Richards flow equation (Celia et al. 1990) which represents mass balance of the fluid phase: 1) r r q q h q r r r r r 0 0 0 1 0 t S s H t c c t H z F = K In this formulation, an infinitely mobile air phase is assumed which in many situations is sufficient for the accurate ....

Celia, M.A., E.T. Bouloutas and R.L. Zarba. 1990. "A general mass conservative numerical solution for the unsaturated flow equation." Water Resources Research 26, no. 7: 1483 - 1496.

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Celia, M.A., E.T. Bouloutas, and R.L. Zarba, "A General Mass- Conservative Numerical Solution for the Unsaturated Flow Equation," Water Resources Research, 26, 1483-1496, 1990.

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M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated ow equation, Water Resour. Res. 26 (1990), 1483-1496.

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M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res. 26 (1990), 1483--1496.

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M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated flow equation, Water Resour. Res., 26(1990), 1483 - 1496.

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M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated ow equation, Water Resour. Res. 26 (1990), 1483-1496.

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M. A. Celia, E. T. Bouloutas, R. L. Zarba, A general mass-conservative numerical solution for the unsaturated ow equation, Water Resour. Res., 26(1990), 1483 - 1496.

No context found.

Michael A. Celia, Efthimios T. Bouloutas, and Rebecca L. Zarba. A general mass-conservativenumerical solution for the unsaturated ow equation. Water Resour. Res., 26(7):1483-1496, jul 1990.

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