R Routines
The routines in the folder fluxLimiters pertain to the solution of the
linear advection equation which is an example of a first order hyperbolic
partial differential equation (PDE). Hyperbolic PDEs can propagate steep
fronts and discontinuities that can make the calculation of an accurate
numerical solution with reasonable computational effort quite challenging.
One approach to the accurate resolution of sharp spatial variations in the
solution of hyperbolic PDEs is the use of a flux limiter to calculate
first order derivatives in the spatial variables. This (fluxLimiter) folder
has R [1] routines for the vanLeer, superbee and smart flux limiters. A
complete example application of the three flux limiters applied to the linear
advection equation taken from [2] is included. The discussion in [2] is
based on Matlab, but the routines in this folder are similar to the Matlab
routines, and a comparison of the two sets of routines (R and Matlab) should
be straightforward. Also, a separate documentation file for the R routines
is under development and should be available later in 2013.
The use of flux limiters is also discussed in detail in Chapter 1 of [3].
Again, the programming is in Matlab, but the comparison of the R and Matlab
routines should be straighforward.
[1] R is an open source, general purpose, scientific computing system that
can be downloaded (gratis) from the Internet: http://cran.fhcrc.org/. Also,
the package deSolve can be downloaded for use with the R routines from the
two books. The editor Rstudio is recommended for use in working with the
routines and for facilitating graphical output: http://rstudio.org/.
[2] Griffiths, G.W. and W.E. Schiesser (2012), Traveling Wave Analysis
of Partial Differential Equations, Chapter 2, Elsevier, New York (see
also http://www.pdecomp.net which includes a download for the Matlab
routines).
[3] Schiessser, W.E. (2013), Partial Differential Equation Analysis in
Biomedical Engineering, Cambridge University Press, Cambridge, UK (see
also http://www.cambridge.org/schiesser which includes a download for the
Matlab routines).
Please direct any questions about the flux limiters to wes1@lehigh.edu.