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(8) This suggests to use a spatial discretization where (Delta z = Delta t) (this corresponds to a Courant-Friedrichs-Lewy (CFL) condition (C = c Delta t/Delta z = 1), c being the speed of light) such that the translation is exact on the lattice.
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The numerical solution consists on approximating (12) into a set of ordinary differential equations using a spatial discretization.
The numerical method caffa3d [1] uses, a spatial discretization based on block-structured, non-orthogonal body fitted grids.
We use a flexible spatial discretization such that complicated conduit networks can be incorporated.
For this comparison we use a particular spatial discretization of the governing transport/reaction partial differential equations (PDEs) based on a stabilized finite element formulation.
In this context we use a particular spatial discretization based on a pressure stabilized Petrov-Galerkin finite element formulation of the low Mach number Navier Stokes equations with heat and mass transport.
For solving the field equations we use an unstructured spatial discretization based on an arbitrary set of nodes situated in the domain.
A spatial discretization using finite differences in two or three dimensions can be employed.
Furthermore, we discuss the general applicability of random walk particle tracking in comparison to the standard transport models and conclude that in advection-dominated problems using a high spatial discretization or requiring the performance of many model runs, RWPT represents a good alternative for modelling contaminant transport.
The study is carried out in the context of a Reynolds averaged Navier Stokes approximation to turbulent fluid flow and heat transfer using a particular spatial discretization based on implicit fully-coupled stabilized FE methods.
We use the spatial discretization of Gibou et al. (2002) [6] for the Poisson equation with Dirichlet boundary conditions, while we use a finite volume discretization for imposing Neumann boundary conditions (Ng et al., 2009; Purvis and Burkhalter, 1979) [8], [10].
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