\name{setup.grid.1D}
\alias{setup.grid.1D}
\alias{plot.grid.1D}
\title{
Creates a One-Dimensional Finite Difference Grid
}
\description{
Subdivides the one-dimensional model domain into one or more zones that
are each sub-divided into grid cells. The resulting grid structure can be
used in the other \code{ReacTran} functions.
The grid structure is characterized by the position of the middle of
the grid cells (\code{x.mid}) and the position of the interfaces between
grid cells (\code{x.int}).
Distances are calculated between the interfaces (\code{dx}), i.e. the
thickness of the grid cells. An auxiliary set of distances (\code{dx.aux})
is calculated between the points where the concentrations are specified
(at the center of each grid cell and the two external interfaces).
A more complex grid consisting of multiple zones can be constructed when
specifying the endpoints of ech zone (\code{x.down}), the interval length
(\code{L}), and the number of layers in each zone (\code{N}) as vectors.
In each zone, one can control the grid resolution near the upstream and
downstream boundary.
The grid resolution at the upstream interface changes according to the
power law relation \code{dx[i+1] = min(max.dx.1,p.dx.1*dx[i])},
where \code{p.dx.1} determines the rate of increase and \code{max.dx.1}
puts an upper limit on the grid cell size.
A similar formula controls the resolution at the downstream interface.
This allows refinement of the grid near the interfaces.
If only \code{x.up, N} and \code{dx.1} are specified, then the grid size
is taken constant = \code{dx.1} (and \code{L=N*dx.1})
}
\usage{
setup.grid.1D(x.up=0, x.down=NULL, L=NULL, N=NULL, dx.1=NULL,
p.dx.1=rep(1,length(L)), max.dx.1=L, dx.N=NULL,
p.dx.N=rep(1,length(L)), max.dx.N=L)
\method{plot}{grid.1D}(x, \dots)
}
\arguments{
\item{x.up }{position of the upstream interface; one value [L]
}
\item{x.down }{position of the endpoint of each zone; one value when the
model domain covers only one zone (\code{x.down} = position of downstream
interface), or a vector of length M when the model domain is divided into
M zones (\code{x.down[M]} = position of downstream interface) [L]
}
\item{L }{thickness of zones; one value (model domain = one zone) or a
vector of length M (model domain = M zones) [L]
}
\item{N }{number of grid cells within a zone; one value or a vector of
length M [-]
}
\item{dx.1 }{size of the first grid cell in a zone; one value or a vector
of length M [L]
}
\item{p.dx.1 }{power factor controlling the increase in grid cell size near
the upstream boundary; one value or a vector of length M. The default
value is 1 (constant grid cell size) [-]
}
\item{max.dx.1 }{maximum grid cell size in the upstream half of the zone;
one value or a vector of length M [L]
}
\item{dx.N }{size of the last grid cell in a zone; one value or a vector
of length M [L]
}
\item{p.dx.N }{power factor controlling the increase in grid cell size near the
downstream boundary; one value or a vector of length M. The default value
is 1 (constant grid cell size) [-]
}
\item{max.dx.N }{maximum grid cell size in the downstream half of the zone;
one value or a vector of length M [L]
}
\item{x }{the object of class \code{grid.1D} that needs plotting
}
\item{...}{additional arguments passed to the function \link{plot}
}
}
\value{
a list of type \code{grid.1D} containing:
\item{N }{the total number of grid cells [-]
}
\item{x.up }{position of the upstream interface; one value [L]
}
\item{x.down }{position of the downstream interface; one value [L]
}
\item{x.mid }{position of the middle of the grid cells;
vector of length \code{N} [L]
}
\item{x.int }{position of the interfaces of the grid cells;
vector of length \code{N+1} [L]
}
\item{dx }{distance between adjacent cell interfaces (thickness of grid
cells); vector of length \code{N} [L]
}
\item{dx.aux }{auxiliary vector containing the distance between adjacent
cell centers; at the upper and lower boundary calculated as
(\code{x[1]-x.up}) and (\code{x.down-x[N]}) respectively; vector of
length \code{N+1} [L]
}
}
\author{
Filip Meysman ,
Karline Soetaert
}
\examples{
# one zone, constant resolution
(GR <- setup.grid.1D(x.up=0,L=10,N=10))
(GR <- setup.grid.1D(x.up=0,L=10,dx.1=1))
(GR <- setup.grid.1D(x.up=0,L=10,dx.N=1))
plot(GR)
# one zone, constant resolution, origin not zero
(GR<-setup.grid.1D(x.up=5,x.down=10,N=10))
plot(GR)
# one zone, variable resolution
(GR <- setup.grid.1D(x.up=0,L=10,dx.1=1,p.dx.1=1.2))
(GR <- setup.grid.1D(x.up=0,L=10,dx.N=1,p.dx.N=1.2))
plot(GR)
# one zone, variable resolution, imposed number of layers
(GR <- setup.grid.1D(x.up=0,L=10,N=6,dx.1=1,p.dx.1=1.2))
(GR <- setup.grid.1D(x.up=0,L=10,N=6,dx.N=1,p.dx.N=1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
(GR<-setup.grid.1D(x.up=0,x.down=10,
dx.1=0.1,p.dx.1=1.2,dx.N=0.1,p.dx.N=1.2))
plot(GR)
# one zone, higher resolution near upstream and downstream interfaces
# imposed number of layers
(GR<-setup.grid.1D(x.up=0,x.down=10, N=20,
dx.1=0.1,p.dx.1=1.2,dx.N=0.1,p.dx.N=1.2))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
(GR<-setup.grid.1D(x.up=0,L=c(5,5),dx.1=c(0.2,0.2),p.dx.1=c(1.1,1.1),
dx.N=c(0.2,0.2),p.dx.N=c(1.1,1.1)))
plot(GR)
# two zones, higher resolution near the upstream
# and downstream interface
# the number of grid cells in each zone is imposed via N
(GR <- setup.grid.1D(x.up=0,L=c(5,5),N=c(20,10),dx.1=c(0.2,0.2),
p.dx.1=c(1.1,1.1),dx.N=c(0.2,0.2),p.dx.N=c(1.1,1.1)))
plot(GR)
}
\keyword{utilities}
\seealso{
\code{\link{tran.1D}}, for a discretisation of the general transport equation in 1-D
\code{\link{setup.grid.2D}} for the creation of grids in 2-D
\code{\link{setup.prop.1D}}, for defining properties on the 1-D grid.
}