Kriging neighbourhood analysis (KNA) was used to determine the most appropriate block size and other estimation parameters such as minimum and maximum samples, discretisation
, to be used for the estimation.
The volume-of-fluid (VoF) method was implemented in a finite volume discretisation
using the open source CFD tool OpenFOAM (Open Source Field Operation and Manipulation).17 The phase field operator was used to capture the air water two-phase flow by determining the fraction of liquid in each mesh element.
where [mathematical expression not reproducible] is the constant of tangential contact, [parallel][v.sup.c.sub.j,[tau]] - [v.sup.c.sub.i,[tau]] is the relative tangential velocity at the point of contact, [DELTA]t is the time interval used in the discretisation
; [micro]s is coefficient of static friction; and [A.sup.c.sub.ij] is interparticle contact area.
"The software will have advanced discretisation
schemes coupled with geo-chemical and geo-mechanical modelling specifically designed for the carbonate nature of Qatar's hydrocarbon reservoirs," said Dr Abushaikha.
The face values of momentum k, [epsilon] were interpolated using the power-law discretisation
scheme and for pressure values second order discretisation
scheme was applied.
An example is the uncertainty associated with the limitations of numerical methods used to construct simulation models, for instance in model discretisation
such as meshing [38, 39].
. We first consider the Taylor-Hood discretisation
using the following approximation spaces
Because of the fixed fluid discretisation
, the fluid velocity at the position X is obtained from convolution with suitably chosen [delta] function
The estimation for Hausdorff distance between the set of trajectories and its approximation depending of the discretisation
and system's parameters is given.
An et al., "Modelling rock fracturing and blast-induced rock mass failure via advanced discretisation
within the discontinuous deformation analysis framework," Computers and Geotechnics, vol.
H-matrices provide a datasparse way to approximate dense matrices arising from the discretisation
of integral operators.