A moving‐mesh finite‐volume method to solve free‐surface seepage problem in arbitrary geometries

Abstract

SUMMARYThe main objective of this work is to develop a novel moving-mesh finite-volume method capable of solving the seepage problem in domains with arbitrary geometries. One major difficulty in analysing the seepage problem is the position of phreatic boundary which is unknown at the beginning of solution. In the current algorithm, we first choose an arbitrary solution domain with a hypothetical phreatic boundary and distribute the finite volumes therein. Then, we derive the conservative statement on a curvilinear co-ordinate system for each cell and implement the known boundary conditions all over the solution domain. Defining a consistency factor, the inconsistency between the hypothesis boundary and the known boundary conditions is measured at the phreatic boundary. Subsequently, the preceding mesh is suitably deformed so that its upper boundary matches the new location of the phreatic surface. This tactic results in a moving-mesh procedure which is continued until the nonlinear boundary conditions are fully satisfied at the phreatic boundary. To validate the developed algorithm, a number of seepage models, which have been previously targeted by the other investigators, are solved. Comparisons between the current results and those of other numerical methods as well as the experimental data show that the current moving-grid finite-volume method is highly robust and it provides sufficient accuracy and reliability.

Unconfined seepage analysis in earth dams using smoothed fixed grid finite element method

“…The main objective of an unconfined seepage problem is to determine the shape and location of phreatic surface. The piezometric head in the wet region Ω of the dam can be calculated as follows 4 where p , ρ and g are fluid pressure, fluid density and the gravitational acceleration, respectively. The fluid velocity vector v , can be obtained as where k ( x ) is the permeability matrix.…”

“…it has poor performance in nonlinear problems and inhomogeneous materials. Finite Difference Method (FDM) 3 and Finite Volume Method (FVM) 4 have also been used in the solution of USPs. In addition to these approaches, the Finite Element Method (FEM), has been widely used to analyze the seepage problem because of its advantages in treating irregular geometries 5, 6.…”

Efficient water table evolution discretization using domain transformation

“…This way, the computational domain is able to follow the dynamic geometry of the saturated region [6]. However, this approach can be computationally demanding for three-dimensional problems and furthermore, large deformations of the domain may cause instabilities [3].…”

Energy‐work‐based numerical manifold seepage analysis with an efficient scheme to locate the phreatic surface

“…A number of numerical methods have been used for modeling unconfined seepage with the phreatic surface. These methods include (i) adaptive‐mesh methods (involving finite difference , finite element , boundary element , and finite volume methods) and (ii) fixed‐mesh methods (involving finite element , finite difference , element‐free , and numerical manifold methods (NMMs) ). Generally, the adaptive‐mesh methods require modifications of the computational mesh for updating the geometry of the simulation domain bounded by the phreatic surface.…”