Home

Context Navigation

Version 2 (modified by fricke, 12 years ago) (diff)
--

Non-cyclic lateral boundary conditions

Figure 1 shows the grid structure for non-cyclic boundary conditions at the left/right boundary LB/RB (bc_lr) and figure 2 for non-cyclic boundary conditions at the north/south boundary NB/SB (bc_ns). The indices (i,j,k) represent the directions (x,y,z). The model domain extends from -1:nx+1 in the x-direction, from -1:ny+1 in the y-direction and from 0:nzt+1 in the z-direction. For the advection scheme of Wicker and Skamarock, two more grid points are added at the lateral boundaries which are not needed for non-cyclic boundary conditions. The figures display the grid layer of the horizontal velocity components u and v, and scalar s. The grid points of the vertical velocity w are defined at the scalar position but shifted by one half grid spacing in vertical direction (not shown, detailed information about the grid structure in PALM can be found here). The prognostic equations are solved at all inner grid points which are marked black. The grid points at the respective non-cyclic boundaries (blue) are treated as follows.

Figure 1: Grid structure at the lateral boundaries with non-cyclic lateral boundary conditions along the left-right direction.

Figure 2: Grid structure of the lateral boundaries with non-cyclic lateral boundary conditions along the north-south direction.

LB is defined at i = -1 for v, w, s and at i = 0 for u. SB is defined at j = -1 for u, w, s and at j = 0 for v. RB is defined at i = nx + 1 and NB at j = ny + 1 for all quantities. LB and SB are treated this way so that the order and number of grid points for the streamwise velocity component and scalars is the same, independent of the flow direction.
For technical reasons, the prognostic equations are first solved for u at i = 0 (v at j = 0), since these grid points technically belong to the inner grid, but afterwards, these results at i = 0 (j = 0) are replaced by the respective boundary condition in routine boundary_conds.f90. In case of a Dirichlet condition, the values at i = 0 (j = 0) are taken from i = -1 (j = -1). In case of a radiation boundary condition, the solution of the Sommerfeld equation overwrites the prognostic values at i = 0 (j = 0).
For non-cyclic lateral boundary conditions, the parameter psolver has to be set to 'multigrid' because the default FFT-solver can only be applied for cyclic boundary conditions.

Inflow boundary

At the inflow boundary, Dirichlet conditions are used for the three velocity components ψ = {u,v,w} as well as for all scalar quantities s and are implemented as follows (here e.g. for s and a flow in positive x direction):

TracMath macro processor has detected an error. Please fix the problem before continuing.

The command:

'/usr/bin/pdflatex -interaction=nonstopmode b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.tex'

failed with the following output:

"This is pdfTeX, Version 3.1415926-2.5-1.40.14 (TeX Live 2013)\n restricted \\write18 enabled.\nentering extended mode\n(./b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.tex\nLaTeX2e <2011/06/27>\nBabel <3.9h> and hyphenation patterns for 78 languages loaded.\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/article.cls\nDocument Class: article 2007/10/19 v1.4h Standard LaTeX document class\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/size10.clo))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/inputenc.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/utf8.def\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1enc.dfu)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/ot1enc.dfu)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/omsenc.dfu)))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/cmap/cmap.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/cm-super/type1ec.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1cmr.fd))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/fontenc.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/base/t1enc.def)<<t1.cmap\n>>) (/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsmath.sty\nFor additional information on amsmath, use the `?' option.\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amstext.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsgen.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsbsy.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsmath/amsopn.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amscls/amsthm.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/amssymb.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/amsfonts.sty))\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/tools/bm.sty)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/preview/preview.sty\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/preview/prtightpage.def)\n)\nNo file b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.aux.\nPreview: Fontsize 10pt\nPreview: PDFoutput 1\n! Missing $ inserted.\n<inserted text> \n                $\nl.14 s^\n       {t + \\Delta t}(k,j,-1) = s_{init}(k) \\; .\n<<ot1.cmap>><<oml.cmap>><<oms.cmap>><<omx.cmap>>\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/umsa.fd)\n(/localdata/software/texlive/2013/texmf-dist/tex/latex/amsfonts/umsb.fd)\n! Missing $ inserted.\n<inserted text> \n                $\nl.15 \\end{preview}\n                  \nPreview: Tightpage -32891 -32891 32891 32891\n[1{/localdata/software/texlive/2013/texmf-var/fonts/map/pdftex/updmap/pdftex.ma\np}] (./b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.aux) )\n(see the transcript file for additional information){/localdata/software/texliv\ne/2013/texmf-dist/fonts/enc/dvips/cm-super/cm-super-t1.enc}</localdata/software\n/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></localdata/\nsoftware/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi7.pfb></loc\naldata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pf\nb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfonts/cm/c\nmr7.pfb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public/amsfont\ns/cm/cmsy10.pfb></localdata/software/texlive/2013/texmf-dist/fonts/type1/public\n/cm-super/sfrm1000.pfb>\nOutput written on b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.pdf (1 page, 52565 b\nytes).\nTranscript written on b3ed5898f0afe2132f91ebe52ab31c8872fcf74a.log.\n"

t denotes the time, Δt the time step and s_init the initialization profile of the scalar quantities which is constant in time. The quantities at the inflow are set by the initial vertical profiles (see initializing_actions). A Neumann condition is used for the subgrid-scale turbulent kinetic energy e (here e.g. for a left-right flow):