A 2D parallel algorithm using MPICH for calculation of ground water flux at evaporation from water table

Abstract

This paper discusses the calculation of distribution of hydraulic head H (x, y), [m] in flux of ground water, which is described by the known steady state groundwater flow equation with nonlinear boundary condition at unknown surface boundary. A special iterative algorithm for a numerical solution of the finite-difference approximation of the above-stated problem using known Richardson's over-relaxation method has been developed. The algorithm for parallel calculation is developed using message passing interface (MPI) for two dimensional case. It has been shown by calculation that above insertion with small coefficient of filtration, a local depression of water surface has been formed. This is the area without outflow of ground water. It may substantially cause the growth of soil salinization above surface of that depression due to evaporation of ground water, as dissolved salt stays in soil layer. Dependencies of the process on evaporation rate and depth of insertion are also discussed. An approximate 58% efficiency in time was obtained using four processes in cluster using message passing interface.

Parallel stabilized mixed Galerkin method for three-dimensional Darcy flow using OpenMP

“…is a space of squareintegrable functions and their divergences, and is a Sobolev space of square-integrable functions and their derivatives of order one [3,10]. Let and be the onedimensional spaces for velocity and pressure respectively, defined as,…”

“…In (10), and are the approximate Darcy velocity and pressure, respectively and and are discrete trial functions. In Galerkin method, these discrete functions can be defined as, (11) , (12) where, is the dimension of the finite subspaces, and and are the unknown coefficient vectors of the finite subspace basis functions.…”

“…For instance, Hussain et al has investigated parallel implementation of stabilized mixed finite element method for two-dimensional Darcy flow using distributed framework [8,9]. The parallel models of ground water flux at evaporation from water table have been studied using MPICH-based algorithms [10,11]. In parallel programming, the shared memory architecture uses single memory space for all the participating processors.…”

Stabilized Mixed Finite Element Method for Transient Darcy Flow

“…For given properties of the fluid and the porous medium, the Darcy model postulates a direct relationship between the fluid flux (or the velocity) and the pressure gradient. The model has been applied to a number of simulations, such as groundwater flow, flow of petroleum in reservoirs and underground solute transport [2][3][4][5][6]. The classical Darcy flow model assumes constant velocity at a given point in space with respect to time.…”

Validating numerical solution of transient Darcy flow using the stabilized mixed finite element method

“…The two-dimensional numerical solution of the Darcy flow for unknown pressure and velocity has been obtained successfully using the stabilized mixed Galerkin method. 5–8 A numerical approach for the solution of nonlinear Darcy flow has also been presented in Yang et al 9 Many real life examples, such as the petroleum flow in reservoirs, the flow in fractured formation of shale reservoirs, the groundwater flow in aquifers and the plasma filtration through blood artery walls, exhibit transient behavior. 10–15 This transient behavior can be incorporated into the Darcy model by adding a time derivative of the pressure.…”