Data · dataset · 2020
Data for: Runge-Kutta-Gegenbauer methods for advection-diffusion problems
Listed in Teesside University Research Data Repository
frkg2.tgz is a C implementation of FRKG numerical integration at second order.
Description
The code consists of two files: the file frkgcore.c contains the code necessary to obtain a solution to the problem prescribed in frkguser.c. The files Tables_N1-N2/arks_<N>_<a>_<b>.csv contain the coefficents for FRKG schemes at orders N=1...2 and, at each order, over a range of 18 Gegenbauer coefficient values running from 0 to 2N.
The coefficients for each scheme is provided for up to Nx257 stages. The default problem is similar to the Brusselator presented by Hairer & Wanner (see (1.6) of Sect. IV.1): a stiff nonlinear diffusion-reaction problem describing chemical kinetics of a tri-molecular chemical reaction subject to periodic boundary conditions.
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Advection is added following Abdulle & Vilmart (2013). The problem is specified via three user defined functions: deriv() - populates f(W)=W_t; spec() - returns spectral radius; and Wexact(). User parameters are: RTOL - error tolerence; NE - number of grid points (including boundary) assuming a uniform square mesh; TEND; XMAX; XMIN.
To apply the FRKG scheme to other problems it should only be necessary to supply a modified version of frkguser.c. Note that complex variables are used via complex.h internally to the time-marching function trystep(). Above trystep() no complex variables are visible.
Usage: to compile executable frkg using gcc gcc -O3 frkgcore.c frkguser.c -lm -o frkg Solution is written to sol.dat Reference solution is sol.ref To plot first species via gnuplot: splot "sol.dat" every 10:10 u 1:2:3 w pm3d ----------------------------- The additional files Tables_N3-N8/arks_<N>_<a>_<b>.csv contain the coefficents for FRKG schemes at orders N=3...8 and, at each order, over a range of 18 Gegenbauer coefficient values running from 0 to 2N.
The coefficients for each scheme is provided for up to Nx257 stages.
Links
Where it is published
- DOI doi.org/10.17632/vk23xxvg7w.1 ↗
DOI / persistent id · from researchdata tees ac uk
Catalogue records · 1
- OAI-PMH record data.mendeley.com/oai?verb=GetRecord&metadataPrefix=oai_dc&identifier=oai%3Adata… ↗
metadata API · from researchdata tees ac uk
Topics
- From keywords
- Earth & Environmental Science · Numerical analysis · Physics
Provenance · 1 source records, 7 field assertions
| Source | Key | Last seen | Raw |
|---|---|---|---|
| Teesside University Research Data Repository | oai:data.mendeley.com/vk23xxvg7w.1 | 20 h ago | JSON v1 |
| Field | Assertion | Extractor | Evidence |
|---|---|---|---|
| concepts[field].anzsrc:field:490302 | mapping · researchdata tees ac uk | vocabulary-mapper@1.0.0 | keywords['Numerical Analysis'] |
| concepts[field].local:field:earth-environmental | mapping · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | |
| concepts[field].local:field:physics | mapping · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | |
| description | source · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | /metadata/dc/description |
| license_text | source · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | |
| publication_date | source · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | |
| title | source · researchdata tees ac uk | connector:researchdata_tees_ac_uk@1.0.0 | /metadata/dc/title |