The PPR package is a Fortran-90 library designed to compute high-order piecewise polynomial reconstructions and conservative integral re-mappings on structured grids. These operators can be used to build high-order finite-volume / arbitrary lagrangian-eulerian ALE schemes for the solution of hyperbolic transport problems.
Various conservative polynomial reconstructions are supported, including piecewise constant PCM, linear PLM, parabolic PPM and quartic PQM types. Each interpolant can be combined with a selection of slope-limiters, including exact monotonicity-preserving and weighted essential non-oscillatory WENO-like formulations. Support is provided for both uniform and non-uniform structured grid types.
The PPR package is encapsulated in a single module: ppr_1d --- defining interfaces to the main reconstruction and re-mapping routines rcon1d and rmap1d. To call PPR, simply #include ../src/ppr_1d.f90 and compile with the -cpp flag.
See the example programs for additional detail.
A set of simple example programs are provided in the ../example directory. See the various inline comments for a detailed description of PPR functionality, data-structures, etc.
ex_1.f90 ! a simple, analytical unit test
ex_2.f90 ! impose monotone slope limiting
ex_3.f90 ! a smooth profile used for convergence tests
ex_4.f90 ! multi-tracer re-mapping
ex_5.f90 ! building high-order interpolants
ex_6.f90 ! flux-form semi-lagrangian transport (in 1d)
ex_7.f90 ! as per ex-1, but with negative orientations
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