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Efforts were further made to settle pastoralists through imposition of boundaries, gazetting of land for game and forest reserves, restriction of movement to dry season grazing areas, forced de-stocking, marginalization of customary institutions and commons governance, and the intensification of sedentary farming (Nsamba 2013).
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This process will greatly simplify the imposition of boundary conditions by the vector potential approach.
Some important factors in the numerical solution of the model equations, namely proper representation of geometry, imposition of boundary conditions and the choice of turbulence model, are discussed.
Imposition of boundary conditions in the MD and DPD systems involves particle insertion and deletion, specular wall reflection and body force terms.
The imposition of boundary conditions exactly on a sharp interface that passes through the Cartesian grid is performed using simple stencil readjustments in the vicinity of the interface.
The key aspects that need to be considered in developing such a solver are imposition of boundary conditions on the immersed boundaries and accurate discretization of the governing equation in cells that are cut by these boundaries.
An important step is a simple low-cost iterative procedure for the Euler Lagrange coupling yielding a substantially better imposition of boundary conditions at the interface, even for large time steps.
In this sense, a separated imposition of boundary conditions for flow and acoustic scales which allows the evacuation of waves through Dirichlet boundaries without using any tailored damping model will be presented.
Typical difficulties lie in the treatment of singularity in the geometrical source and the imposition of boundary conditions at the symmetric center, in addition to the resolution of classical discontinuities (shocks and contact discontinuities).
Summation-by-Parts (SBP) operators for the space and time discretization, together with a weak imposition of boundary and initial conditions using Simultaneously Approximation Terms (SATs) lead to a provable fully-discrete energy-stable conservative finite difference scheme.
In addition, as B-spline basis functions pose favorable properties such as (i) easy to construct to any arbitrary order/degree, (ii) have partition of unity property, and (iii) can be easily designed to pose the Kronecker delta property, the shape function construction as well as the imposition of boundary conditions can be incorporated efficiently in the present method.
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