\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. }