Mathematical development and verification of a non-orthogonal finite volume model for groundwater flow applications

Nonlinear Multigrid Methods for Numerical Solution of the Unsaturated Flow Equation in Two Space Dimensions

“…Finite differences (Haverkamp et al 1977;Celia et al 1990; Lee et al 2004;McDonald and Harbaugh 2008) Galerkin finite element (Pinder and Gray 1977;Lin et al 1997) mixed finite element (Baca et al 1997;Berganaschi and Putti 1999;Woodward and Dawson 2000), and finite volumes (Eymard et al 1999(Eymard et al , 2000Manzini and Ferraris 2004;Loudyi et al 2007) are the standard approximations employed for the discretization of the spatial derivatives. The spatial discretization is coupled with the method of lines for the time discretization.…”

Finite Volume Method of Modelling Transient Groundwater Flow

“…The accuracy of a control volume discretization depends heavily on the approximation of the ux at the midpoint of the control volume faces and many methods have been proposed to approximate the gradient along a control volume surface for different computational fluid dynamics applications (Loudyi et al, 2007;Jayantha and Turner, 2001;2003). To calculate the gradients at the midpoint of the cell faces, an approximate distribution of properties between nodal points is used (Versteeg and Malalasekera, 1995).…”

3D finite volume groundwater and heat transport modeling with non-orthogonal grids, using a coordinate transformation method

“…In contrast to Loudyi et al [17] we do not use grids which are randomly disturbed to obtain non-orthogonality, because in our opinion numerical errors are more easy to detect when a regular deformed grid is applied. However, the following test is very similar to the Kershaw test which the above mentioned authors have applied also.…”

“…Lately, Loudyi et al [17] have presented a code which uses also a FVM on non-orthogonal grids. In contrast to our approach they use an improved least squares gradient technique to take the non-orthogonality into account.…”