Soil mechanics uses the cubic differential element, whereas the particle method considers spherical elements in the discretisation
In the subsequent mechanical analysis phases, discretisation
error and other software error are important issues to assess.
Hybrid discontinuous Galerkin discretisation
. We restrict the discussion to the two dimensional case d = 2.
A second-order accurate discretisation
and a unified formalism for fluid-particle interactions including dissipative coupling, immersed boundary method, and external boundary were derived by Schiller .
This is because the vertical normal force is transmitted down to the sleeper and to the ground without affecting by the rail bending stiffness, discretisation
of the track, and the formation of the turnout.
One contact pair was set up in the finite element model, namely, the outer surface of the roll body and the top surface of the strip, which was defined as frictional interface adopting a friction coefficient of 0.15, as well as applying the finite sliding formulation and surface-to-surface discretisation
approach to obtain a stress accuracy improvement [5, 54].
of a basin plays an important role in the modelling process as it provides more detailed and realistic outcomes.
Most commercial codes  have an algebraic VOF solver available (where a typical discretisation
method is used to convect the VOF value), often with special numerical techniques for sharpening the interface between phases.
The derived optimization task for the heat conduction problem represents an implicit method, whose stability does not impose any stability criteria in time or space discretisation
. Hence, the maximum time step is only limited by the required accuracy.
This part of the paper deals with the discretisation
of mathematical apparatus for different control methods.
Because of the identical mesh adopted in both CFD models, the assessment was focused on the differences in numerical discretisation
and models implemented within the two computer codes.
The predominant advantage of this method is that it can be applied directly to linear and nonlinear ordinary differential equations without requiring linearisation, discretisation
, or perturbation .