diff options
| author | rhaas <rhaas@c83d129a-5a75-4d5a-9c4d-ed3a5855bf45> | 2011-11-04 18:34:36 +0000 |
|---|---|---|
| committer | rhaas <rhaas@c83d129a-5a75-4d5a-9c4d-ed3a5855bf45> | 2011-11-04 18:34:36 +0000 |
| commit | eb1d76b0841fa77d7158ec8392d5dcfbfba8949e (patch) | |
| tree | 456e08a4aac4f9fd3e478a456c9a6fe01f2dd79e /doc | |
| parent | a2b91f57094795a9f825c5279f8962d52a7e3f8c (diff) | |
second iteration of constraint transport
* fix some indices
* move poison loop to proper spot
* compute conserved divergence in track_divB
* add Maple worksheet to check constraint transport indices
git-svn-id: http://svn.einsteintoolkit.org/cactus/EinsteinEvolve/GRHydro/trunk@298 c83d129a-5a75-4d5a-9c4d-ed3a5855bf45
Diffstat (limited to 'doc')
| -rw-r--r-- | doc/constraint_transport.mw | 268 |
1 files changed, 268 insertions, 0 deletions
diff --git a/doc/constraint_transport.mw b/doc/constraint_transport.mw new file mode 100644 index 0000000..020e75c --- /dev/null +++ b/doc/constraint_transport.mw @@ -0,0 +1,268 @@ +<?xml version="1.0" encoding="UTF-8"?> +<Worksheet> +<Version major="15" minor="0"/> +<Label-Scheme value="2" prefix=""/> +<View-Properties presentation="false"><Zoom percentage="200"/></View-Properties> +<MapleNet-Properties elisiondigitsbefore="100" labelling="true" indentamount="4" elisiontermsthreshold="10000" ansi="false" errorbreak="1" useclientjvm="true" echo="1" imaginaryunit="I" labelwidth="20" contextmenusize="automatic" plotdriver="opengl" elisiondigitsafter="100" plotoutput="terminal" helpbrowser="standard" rtablesize="10" elisiontermsbefore="100" elisiondigitsthreshold="10000" typesetting="standard" plotdevice="inline" verboseproc="1" showassumed="1" errorcursor="false" longdelim="true" plotoptions="" quiet="false" elisiontermsafter="100" screenwidth="79" preplot="" prettyprint="3" displayprecision="-1" screenpixelheight="1080" warnlevel="3" screenheight="25" latexwidth="6.0" postplot="" prompt="> " ShowLabels="true"/> +<Styles><Font name="Ordered List 1" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/> +<Font name="Annotation Text" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/> +<Font name="Ordered List 2" background="[255,255,255]" bold="false" executable="false" family="Times New Roman" foreground="[0,0,0]" italic="false" opaque="false" readonly="false" size="12" subscript="false" superscript="false" underline="false" placeholder="false"/> +<Font name="Ordered List 3" 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name="Pencil 1" pen-color="[0,0,0]" pen-height="1.0" pen-width="1.0" pen-opacity="1.0"/> +<Highlighter-style name="Highlighter 2" pen-color="[255,204,0]" pen-height="14.0" pen-width="14.0" pen-opacity="0.8"/> +<Highlighter-style name="Highlighter 1" pen-color="[255,153,255]" pen-height="12.0" pen-width="8.0" pen-opacity="0.8"/> +<Highlighter-style name="Highlighter 4" pen-color="[0,255,255]" pen-height="32.0" pen-width="32.0" pen-opacity="0.8"/> +<Highlighter-style name="Highlighter 3" pen-color="[51,255,0]" pen-height="24.0" pen-width="24.0" pen-opacity="0.8"/> +<Highlighter-style name="Highlighter 5" pen-color="[255,255,0]" pen-height="48.0" pen-width="48.0" pen-opacity="0.8"/> +</Styles> +<Task-table> + <Task-category name="<default>"> + </Task-category> +</Task-table> +<Task> +</Task> +<Group labelreference="L34" drawlabel="true"> +<Input> +<Text-field style="Heading 1" layout="Heading 1"><Font executable="true">Constraint transport scheme in GRHydro</Font></Text-field> +<Text-field style="Text" layout="Heading 1">The current constraint transport scheme in GRHydro is based on WhiskyMHD (arXiv:gr-qc/0701109) and Bruno Giacomazzo's PhD thesis (http://www.sissa.it/ap/PhD/Theses/giacomazzo.ps.gz). It assumes that all magnetic field components live at the cell center and uses the Reconstruction step to move them to the cell interfaces.</Text-field> +<Text-field style="Text" layout="Heading 1"><Font encoding="UTF-8">This worksheet helps checking the expressions entered into the code by explicitely checking that div(\134dot B) = 0.</Font></Text-field> +</Input> +</Group> +<Group labelreference="L3"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">restart;</Text-field> +</Input> +</Group> +<Group labelreference="L4"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal"># we later expand taylor series in eps which helps counting orders in the stepsize +dx:=eps*dX;dy:=eps*dY;dz:=eps*dZ;</Text-field> +</Input> +</Group> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1">Fluxes of the magnetic field components</Text-field></Title> +<Group labelreference="L5"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconsxfluxX := (i,j,k) -> 0;</Text-field> +</Input> +</Group> +<Group labelreference="L6"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconsyfluxX := (i,j,k) -> add(add(add(BconsyfluxX_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3);</Text-field> +</Input> +</Group> +<Group labelreference="L7"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconszfluxX := (i,j,k) -> add(add(add(BconszfluxX_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3);</Text-field> +</Input> +</Group> +<Group labelreference="L8"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal"># enforce F^I(B^j) = -F^j(B^i) if desired to check that RHS computed agrees to some order with the one used in divergence cleaning +BconsxfluxY := (i,j,k) -> add(add(add(BconsxfluxY_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3); #-BconsyfluxX(i,j,k);</Text-field> +</Input> +</Group> +<Group labelreference="L9"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconsyfluxY := (i,j,k) -> 0;</Text-field> +</Input> +</Group> +<Group labelreference="L10"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconszfluxY := (i,j,k) -> add(add(add(BconszfluxY_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3);</Text-field> +</Input> +</Group> +<Group labelreference="L11"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconsxfluxZ := (i,j,k) -> add(add(add(BconsxfluxZ_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3); #-BconszfluxX(i,j,k);</Text-field> +</Input> +</Group> +<Group labelreference="L12"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconsyfluxZ := (i,j,k) -> add(add(add(BconsyfluxZ_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3); #-BconszfluxY(i,j,k);</Text-field> +</Input> +</Group> +<Group labelreference="L13"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">BconszfluxZ := (i,j,k) -> 0;</Text-field> +</Input> +</Group> +</Section> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1">Lapse</Text-field></Title> +<Group labelreference="L14"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">alp := (i,j,k) -> add(add(add(alp_coeff[_i,_j,_k] * (i*dx)^_i * (j*dy)^_j * (k*dz)^_k,_i=0..3),_j=0..3),_k=0..3);</Text-field> +</Input> +</Group> +</Section> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1"><Font encoding="UTF-8">Electric fields (eventually from E=v \134cross B=F(B))</Font></Text-field></Title> +<Group labelreference="L16"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Ey := (i,j,k) -> 1/4*(alp(i+1/2,j,k)*BconszfluxX(i+1/2,j,k) + alp(i+1/2,j,k+1)*BconszfluxX(i+1/2,j,k+1)) - + 1/4*(alp(i,j,k+1/2)*BconsxfluxZ(i,j,k+1/2) + alp(i+1,j,k+1/2)*BconsxfluxZ(i+1,j,k+1/2));</Text-field> +</Input> +</Group> +<Group labelreference="L17"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Ez := (i,j,k) -> 1/4*(alp(i,j+1/2,k)*BconsxfluxY(i,j+1/2,k) + alp(i+1,j+1/2,k)*BconsxfluxY(i+1,j+1/2,k)) - + 1/4*(alp(i+1/2,j,k)*BconsyfluxX(i+1/2,j,k) + alp(i+1/2,j+1,k)*BconsyfluxX(i+1/2,j+1,k));</Text-field> +</Input> +</Group> +<Group labelreference="L18"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Ex := (i,j,k) -> 1/4*(alp(i,j,k+1/2)*BconsyfluxZ(i,j,k+1/2) + alp(i,j+1,k+1/2)*BconsyfluxZ(i,j+1,k+1/2)) - + 1/4*(alp(i,j+1/2,k)*BconszfluxY(i,j+1/2,k) + alp(i,j+1/2,k+1)*BconszfluxY(i,j+1/2,k+1));</Text-field> +</Input> +</Group> +</Section> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1">RHS for B</Text-field></Title> +<Group labelreference="L19"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Bconsrhsx := (i,j,k) -> -1/2*(Ey(i-1,j ,k-1)-Ey(i-1,j ,k ))/dz + -1/2*(Ez(i-1,j ,k )-Ez(i-1,j-1,k ))/dy + -1/2*(Ey(i ,j ,k-1)-Ey(i ,j ,k ))/dz + -1/2*(Ez(i ,j ,k )-Ez(i ,j-1,k ))/dy:</Text-field> +</Input> +</Group> +<Group labelreference="L20"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Bconsrhsy := (i,j,k) -> -1/2 * (Ez(i-1,j-1,k )-Ez(i ,j-1,k )) / dx + -1/2 * (Ex(i ,j-1,k )-Ex(i ,j-1,k-1)) / dz + -1/2 * (Ez(i-1,j ,k )-Ez(i ,j ,k )) / dx + -1/2 * (Ex(i ,j ,k )-Ex(i ,j ,k-1)) / dz:</Text-field> +</Input> +</Group> +<Group labelreference="L21"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Bconsrhsz := (i,j,k) -> - 1/2 * (Ex(i ,j-1,k-1)-Ex(i ,j ,k-1)) / dy + - 1/2 * (Ey(i ,j ,k-1)-Ey(i-1,j ,k-1)) / dx + - 1/2 * (Ex(i ,j-1,k )-Ex(i ,j ,k )) / dy + - 1/2 * (Ey(i ,j ,k )-Ey(i-1,j ,k )) / dx:</Text-field> +</Input> +</Group> +</Section> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1">Check RHS at center of cell</Text-field></Title> +<Group labelreference="L36" drawlabel="true"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">Bconsrhsx(0,0,0):</Text-field> +</Input> +</Group> +<Group labelreference="L23"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">simplify(%):</Text-field> +</Input> +</Group> +<Group labelreference="L24"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">algsubs(eps=0,%);</Text-field> +</Input> +</Group> +<Group labelreference="L37" drawlabel="true"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field> +</Input> +</Group> +<Group labelreference="L40"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">(alp(0,-1/2,0)*BconsxfluxY(0,-1/2,0)-alp(0,1/2,0)*BconsxfluxY(0,1/2,0))/dy + +(alp(0,0,-1/2)*BconsxfluxZ(0,0,-1/2)-alp(0,0,1/2)*BconsxfluxZ(0,0,1/2))/dz:</Text-field> +</Input> +</Group> +<Group labelreference="L39"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">collect(%,eps):algsubs(eps^2=0,%);</Text-field> +</Input> +</Group> +</Section> +<Section collapsed="false" MultipleChoiceAnswerIndex="-1" MultipleChoiceRandomizeChoices="false" TrueFalseAnswerIndex="-1" EssayAnswerRows="5" EssayAnswerColumns="60"><Title> +<Text-field style="Heading 1" layout="Heading 1">Check constraint transport property for edge based divergence operator (see Bruno's thesis)</Text-field></Title> +<Group labelreference="L29"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">divB := (i,j,k) -> (Bconsrhsx(i+1,j,k)-Bconsrhsx(i,j,k)+Bconsrhsx(i+1,j+1,k)-Bconsrhsx(i,j+1,k)+Bconsrhsx(i+1,j,k+1)-Bconsrhsx(i,j,k+1)+Bconsrhsx(i+1,j+1,k+1)-Bconsrhsx(i,j+1,k+1))/4/dx + +(Bconsrhsy(i,j+1,k)-Bconsrhsy(i,j,k)+Bconsrhsy(i+1,j+1,k)-Bconsrhsy(i+1,j,k)+Bconsrhsy(i,j+1,k+1)-Bconsrhsy(i,j,k+1)+Bconsrhsy(i+1,j+1,k+1)-Bconsrhsy(i+1,j,k+1))/4/dy + +(Bconsrhsz(i,j,k+1)-Bconsrhsz(i,j,k)+Bconsrhsz(i+1,j,k+1)-Bconsrhsz(i+1,j,k)+Bconsrhsz(i,j+1,k+1)-Bconsrhsz(i,j+1,k)+Bconsrhsz(i+1,j+1,k+1)-Bconsrhsz(i+1,j+1,k))/4/dz;</Text-field> +</Input> +</Group> +<Group labelreference="L30"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal">simplify(divB(0,0,0));</Text-field> +</Input> +</Group> +</Section> +<Group labelreference="L41" drawlabel="true"> +<Input> +<Text-field prompt="> " style="Maple Input" layout="Normal"></Text-field> +</Input> +</Group> +<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field> +<Text-field superscript="false" placeholder="false" executable="false" selection-placeholder="false" italic="false" size="12" bold="false" subscript="false" family="Times New Roman" opaque="false" underline="false" background="[255,255,255]" readonly="false" foreground="[0,0,0]" alignment="left" firstindent="0" spacebelow="0" leftmargin="0" linespacing="0.0" initial="0" linebreak="space" rightmargin="0" bulletsuffix="" spaceabove="0" bullet="none" pagebreak-before="false"></Text-field> +</Worksheet>
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