Commits (31)
CMAKE_MINIMUM_REQUIRED(VERSION 2.8.7)
PROJECT(Nektar++-Tutorial)
INCLUDE(CMakeParseArguments)
SET(TUTORIAL_ROOT ${CMAKE_CURRENT_SOURCE_DIR})
# Generates PDF and HTML targets for tutorials. These will be named
# <target-base-name>-pdf and <target-base-name>-html.
#
# TARGET <name> Base name of target to create.
# BASE <name> Base name of .tex file.
# STYLING_FILE <file> The HTML styling file to use.
# PDF Generate PDF target.
# HTML Generate HTML target.
# HTML_BREAK_LEVEL <N> Section depth to break into separate files.
# USES_INDEX Run 'makeindex'
# USES_REFS Run 'bibtex'
# ARCHIVE Make tarball of associated files
# First file is archive name, followed by included files.
#
MACRO(ADD_NEKTAR_TUTORIAL)
SET(options PDF HTML USES_INDEX USES_REFS)
SET(oneValueArgs TARGET BASE STYLING_FILE HTML_BREAK_LEVEL)
SET(multiValueArgs ARCHIVE)
cmake_parse_arguments(NEK "${options}"
"${oneValueArgs}" "${multiValueArgs}" ${ARGN} )
SET(NEKSRC ${CMAKE_SOURCE_DIR})
SET(SRC ${CMAKE_CURRENT_SOURCE_DIR})
SET(TGT ${CMAKE_CURRENT_BINARY_DIR})
IF (NEK_PDF)
FIND_PROGRAM(PDFLATEX pdflatex)
FIND_PROGRAM(BIBTEX bibtex)
FIND_PROGRAM(MAKEINDEX makeindex)
MARK_AS_ADVANCED(PDFLATEX BIBTEX MAKEINDEX)
# Main target (Final PDFLatex)
ADD_CUSTOM_TARGET(${NEK_TARGET}-pdf
TEXINPUTS=${NEKSRC}/:${TUTORIAL_ROOT}/shared//:
${PDFLATEX} --output-directory ${TGT} ${SRC}/${NEK_BASE}.tex
WORKING_DIRECTORY ${SRC}
)
# Initial PDFLATEX
ADD_CUSTOM_TARGET(${NEK_TARGET}-pdflatex
TEXINPUTS=${NEKSRC}/:${TUTORIAL_ROOT}/shared//:
${PDFLATEX} --output-directory ${TGT} ${SRC}/${NEK_BASE}.tex
WORKING_DIRECTORY ${SRC})
ADD_DEPENDENCIES(${NEK_TARGET}-pdf ${NEK_TARGET}-pdflatex)
# Bibtex if required
IF (NEK_USES_REFS)
ADD_CUSTOM_TARGET(${NEK_TARGET}-bibtex
COMMAND TEXMFOUTPUT=${TGT} ${BIBTEX} ${TGT}/${NEK_BASE}.aux
WORKING_DIRECTORY ${SRC})
ADD_DEPENDENCIES(${NEK_TARGET}-pdf ${NEK_TARGET}-bibtex)
ADD_DEPENDENCIES(${NEK_TARGET}-bibtex ${NEK_TARGET}-pdflatex)
ENDIF()
# Index if required
IF (NEK_USES_INDEX)
ADD_CUSTOM_TARGET(${NEK_TARGET}-index
COMMAND TEXMFOUTPUT=${TGT} ${MAKEINDEX} ${TGT}/${NEK_BASE}.aux
WORKING_DIRECTORY ${SRC})
ADD_DEPENDENCIES(${NEK_TARGET}-pdf ${NEK_TARGET}-index)
ADD_DEPENDENCIES(${NEK_TARGET}-index ${NEK_TARGET}-pdflatex)
ENDIF()
# Create an archive of the tutorial files
IF (NEK_ARCHIVE)
SET(TARFILE "${TGT}/${NEK_TARGET}.tar.gz")
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-pdf POST_BUILD
COMMAND ${CMAKE_COMMAND} -E tar "cvfz" ${TARFILE}
${NEK_ARCHIVE}
WORKING_DIRECTORY ${SRC}
COMMENT "Generating ${TARFILE}")
ENDIF()
ENDIF ()
IF (NEK_HTML)
FILE(MAKE_DIRECTORY ${TGT}/html)
FIND_PROGRAM(HTLATEX htlatex)
MARK_AS_ADVANCED(HTLATEX)
IF (NOT NEK_HTML_BREAK_LEVEL)
SET(NEK_HTML_BREAK_LEVEL 3)
ENDIF()
# Generate HTML
SET(FLAGS "html,${NEK_HTML_BREAK_LEVEL},next,NoFonts")
IF (NEK_STYLING_FILE)
SET(FLAGS "${NEK_STYLING_FILE},${FLAGS}")
ENDIF()
ADD_CUSTOM_TARGET(${NEK_TARGET}-html
TEXINPUTS=${NEKSRC}/:${SRC}//:${TUTORIAL_ROOT}/shared//:
${HTLATEX} ${SRC}/${NEK_BASE}.tex
"${FLAGS}"
WORKING_DIRECTORY ${TGT}/html
)
# Copy images across
FILE(GLOB_RECURSE imgfiles "img/*.png" "img/*.jpg" "*/img/*.png"
"*/img/*.jpg" "${TUTORIAL_ROOT}/shared/img/*.png"
"${TUTORIAL_ROOT}/shared/img/*.jpg")
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-html POST_BUILD
COMMAND ${CMAKE_COMMAND} -E make_directory ${TGT}/html/img)
FOREACH(img ${imgfiles})
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-html POST_BUILD
COMMAND ${CMAKE_COMMAND} -E copy ${img} ${TGT}/html/img
COMMENT "Copying file ${img} to ${TGT}/html/img...")
ENDFOREACH()
# Convert PDF files and copy across
FILE(GLOB_RECURSE pdffiles "img/*.pdf" "*/img/*.pdf"
"${TUTORIAL_ROOT}/shared/img/*.pdf")
FIND_PROGRAM(CONVERT convert)
MARK_AS_ADVANCED(CONVERT)
FOREACH(pdf ${pdffiles})
GET_FILENAME_COMPONENT(BASENAME ${pdf} NAME_WE)
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-html POST_BUILD
COMMAND ${CONVERT} ${pdf} ${TGT}/html/img/${BASENAME}.png
COMMENT "Converting ${pdf} to PNG...")
ENDFOREACH()
IF (NEK_ARCHIVE)
SET(TARFILE "${TGT}/html/${NEK_TARGET}.tar.gz")
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-html POST_BUILD
COMMAND ${CMAKE_COMMAND} -E tar "cvfz" ${TARFILE}
${NEK_ARCHIVE}
WORKING_DIRECTORY ${SRC}
COMMENT "Generating ${TARFILE}")
FOREACH(f ${NEK_ARCHIVE})
GET_FILENAME_COMPONENT(TGTNAME ${f} NAME)
ADD_CUSTOM_COMMAND(TARGET ${NEK_TARGET}-html POST_BUILD
COMMAND ${CMAKE_COMMAND} -E copy_directory ${f}
${TGT}/html/${TGTNAME}
COMMENT "Copying file ${f} to ${TGT}/html/${TGTNAME}...")
ENDFOREACH()
ENDIF()
ENDIF()
ENDMACRO()
MACRO(ADD_NEKTAR_TUTORIAL_TEST solver testname)
GET_FILENAME_COMPONENT(dir ${CMAKE_CURRENT_SOURCE_DIR} NAME)
ADD_TEST(NAME ${dir}_${testname}
COMMAND $<TARGET_FILE:Tester> -e $<TARGET_FILE:${solver}>
${CMAKE_CURRENT_SOURCE_DIR}/tests/${testname}.tst)
ENDMACRO()
ADD_SUBDIRECTORY(events)
ADD_SUBDIRECTORY(flow-stability)
Nektar++/tutorial
========
Nektar++/tutorial contains some useful tutorials associated to the open-source
software framework Nektar++.
The software is designed to support the development of high-performance scalable
solvers for partial differential equations (PDEs) using the spectral/hp element
method.
The tutorials are still under development and will become available shortly.
Note that the User Guide is available for download from <http://www.nektar.info/>.
ADD_SUBDIRECTORY(Cambridge-AIM)
ADD_NEKTAR_TUTORIAL(PDF HTML TARGET 2011-Cambridge-AIM BASE CambridgeTutorial
STYLING_FILE ${TUTORIAL_ROOT}/styling.cfg HTML_BREAK_LEVEL 2)
# Add tests only if we are building from within the Nektar++ tree
IF (DEFINED NEKTAR_BUILD_TESTS)
MESSAGE(STATUS "Will do tests")
ENDIF()
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Point(1) = {3.141592653589793, -1, 0, 1e+22};
Point(2) = {3.141592653589793, 1, 0, 1e+22};
Point(3) = {-3.141592653589793, 1, 0, 1e+22};
Point(4) = {-3.141592653589793, -1, 0, 1e+22};
Line(1) = {4, 1};
Line(2) = {1, 2};
Line(3) = {2, 3};
Line(4) = {3, 4};
Line Loop(5) = {2, 3, 4, 1};
Plane Surface(6) = {5};
Transfinite Line {1, 3} = 9 Using Progression 1;
Transfinite Line {4, 2} = 7 Using Bump 0.2;
Transfinite Surface {6};
Recombine Surface {6};
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<?xml version="1.0" encoding="utf-8" ?>
<NEKTAR>
<CONDITIONS>
<SOLVERINFO>
<I PROPERTY="SolverType" VALUE="VelocityCorrectionScheme"/>
<I PROPERTY="EQTYPE" VALUE="UnsteadyNavierStokes"/>
<I PROPERTY="EvolutionOperator" VALUE="Nonlinear"/>
<I PROPERTY="Projection" VALUE="Continuous"/>
<I PROPERTY="TimeIntegrationMethod" VALUE="IMEXOrder3"/>
<I PROPERTY="Driver" VALUE="Standard"/>
</SOLVERINFO>
<PARAMETERS>
<P> TimeStep = 0.001 </P>
<P> NumSteps = 1000 </P>
<P> IO_CheckSteps = 500 </P>
<P> IO_InfoSteps = 10 </P>
<P> Kinvis = 1.0/7500 </P>
</PARAMETERS>
<VARIABLES>
<V ID="0"> u </V>
<V ID="1"> v </V>
<V ID="2"> p </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[3] </B>
<B ID="2"> C[2] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" VALUE="0" />
<D VAR="v" VALUE="0" />
<N VAR="p" USERDEFINEDTYPE="H" VALUE="0"/> // High Order Pressure BC
</REGION>
<REGION REF="1">
<P VAR="u" VALUE="[2]" />
<P VAR="v" VALUE="[2]" />
<P VAR="p" VALUE="[2]" /> // High Order Pressure BC
</REGION>
<REGION REF="2">
<P VAR="u" VALUE="[1]" />
<P VAR="v" VALUE="[1]" />
<P VAR="p" VALUE="[1]" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="BodyForce">
<E VAR="u" VALUE="2*Kinvis" />
<E VAR="v" VALUE="0" />
<E VAR="p" VALUE="0" />
</FUNCTION>
<FUNCTION NAME="InitialConditions">
<E VAR="u" VALUE="-(y+1)*(y-1)" />
<E VAR="v" VALUE="0" />
<E VAR="p" VALUE="0" />
</FUNCTION>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="-(y+1)*(y-1)" />
<E VAR="v" VALUE="0" />
<E VAR="p" VALUE="0" />
</FUNCTION>
</CONDITIONS>
<GEOMETRY DIM="2" SPACE="2">
<VERTEX>
<V ID="0">3.142e+00 1.000e+00 0.000e+00</V>
<V ID="1">2.356e+00 1.000e+00 0.000e+00</V>
<V ID="2">2.356e+00 8.000e-01 0.000e+00</V>
<V ID="3">3.142e+00 8.000e-01 0.000e+00</V>
<V ID="4">2.356e+00 5.000e-01 0.000e+00</V>
<V ID="5">3.142e+00 5.000e-01 0.000e+00</V>
<V ID="6">2.356e+00 -1.561e-12 0.000e+00</V>
<V ID="7">3.142e+00 -2.082e-12 0.000e+00</V>
<V ID="8">2.356e+00 -5.000e-01 0.000e+00</V>
<V ID="9">3.142e+00 -5.000e-01 0.000e+00</V>
<V ID="10">2.356e+00 -8.000e-01 0.000e+00</V>
<V ID="11">3.142e+00 -8.000e-01 0.000e+00</V>
<V ID="12">2.356e+00 -1.000e+00 0.000e+00</V>
<V ID="13">3.142e+00 -1.000e+00 0.000e+00</V>
<V ID="14">1.571e+00 1.000e+00 0.000e+00</V>
<V ID="15">1.571e+00 8.000e-01 0.000e+00</V>
<V ID="16">1.571e+00 5.000e-01 0.000e+00</V>
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<V ID="18">1.571e+00 -5.000e-01 0.000e+00</V>
<V ID="19">1.571e+00 -8.000e-01 0.000e+00</V>
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<V ID="30">1.850e-12 5.000e-01 0.000e+00</V>
<V ID="31">-1.110e-16 5.551e-17 0.000e+00</V>
<V ID="32">-1.850e-12 -5.000e-01 0.000e+00</V>
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<V ID="37">-7.854e-01 5.000e-01 0.000e+00</V>
<V ID="38">-7.854e-01 5.203e-13 0.000e+00</V>
<V ID="39">-7.854e-01 -5.000e-01 0.000e+00</V>
<V ID="40">-7.854e-01 -8.000e-01 0.000e+00</V>
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<V ID="55">-2.356e+00 -1.000e+00 0.000e+00</V>
<V ID="56">-3.142e+00 1.000e+00 0.000e+00</V>
<V ID="57">-3.142e+00 8.000e-01 0.000e+00</V>
<V ID="58">-3.142e+00 5.000e-01 0.000e+00</V>
<V ID="59">-3.142e+00 2.082e-12 0.000e+00</V>
<V ID="60">-3.142e+00 -5.000e-01 0.000e+00</V>
<V ID="61">-3.142e+00 -8.000e-01 0.000e+00</V>
<V ID="62">-3.142e+00 -1.000e+00 0.000e+00</V>
</VERTEX>
<EDGE>
<E ID="0"> 0 1 </E>
<E ID="1"> 1 2 </E>
<E ID="2"> 2 3 </E>
<E ID="3"> 3 0 </E>
<E ID="4"> 2 4 </E>
<E ID="5"> 4 5 </E>
<E ID="6"> 5 3 </E>
<E ID="7"> 4 6 </E>
<E ID="8"> 6 7 </E>
<E ID="9"> 7 5 </E>
<E ID="10"> 6 8 </E>
<E ID="11"> 8 9 </E>
<E ID="12"> 9 7 </E>
<E ID="13"> 8 10 </E>
<E ID="14"> 10 11 </E>
<E ID="15"> 11 9 </E>
<E ID="16"> 10 12 </E>
<E ID="17"> 12 13 </E>
<E ID="18"> 13 11 </E>
<E ID="19"> 1 14 </E>
<E ID="20"> 14 15 </E>
<E ID="21"> 15 2 </E>
<E ID="22"> 15 16 </E>
<E ID="23"> 16 4 </E>
<E ID="24"> 16 17 </E>
<E ID="25"> 17 6 </E>
<E ID="26"> 17 18 </E>
<E ID="27"> 18 8 </E>
<E ID="28"> 18 19 </E>
<E ID="29"> 19 10 </E>
<E ID="30"> 19 20 </E>
<E ID="31"> 20 12 </E>
<E ID="32"> 14 21 </E>
<E ID="33"> 21 22 </E>
<E ID="34"> 22 15 </E>
<E ID="35"> 22 23 </E>
<E ID="36"> 23 16 </E>
<E ID="37"> 23 24 </E>
<E ID="38"> 24 17 </E>
<E ID="39"> 24 25 </E>
<E ID="40"> 25 18 </E>
<E ID="41"> 25 26 </E>
<E ID="42"> 26 19 </E>
<E ID="43"> 26 27 </E>
<E ID="44"> 27 20 </E>
<E ID="45"> 21 28 </E>
<E ID="46"> 28 29 </E>
<E ID="47"> 29 22 </E>
<E ID="48"> 29 30 </E>
<E ID="49"> 30 23 </E>
<E ID="50"> 30 31 </E>
<E ID="51"> 31 24 </E>
<E ID="52"> 31 32 </E>
<E ID="53"> 32 25 </E>
<E ID="54"> 32 33 </E>
<E ID="55"> 33 26 </E>
<E ID="56"> 33 34 </E>
<E ID="57"> 34 27 </E>
<E ID="58"> 28 35 </E>
<E ID="59"> 35 36 </E>
<E ID="60"> 36 29 </E>
<E ID="61"> 36 37 </E>
<E ID="62"> 37 30 </E>
<E ID="63"> 37 38 </E>
<E ID="64"> 38 31 </E>
<E ID="65"> 38 39 </E>
<E ID="66"> 39 32 </E>
<E ID="67"> 39 40 </E>
<E ID="68"> 40 33 </E>
<E ID="69"> 40 41 </E>
<E ID="70"> 41 34 </E>
<E ID="71"> 35 42 </E>
<E ID="72"> 42 43 </E>
<E ID="73"> 43 36 </E>
<E ID="74"> 43 44 </E>
<E ID="75"> 44 37 </E>
<E ID="76"> 44 45 </E>
<E ID="77"> 45 38 </E>
<E ID="78"> 45 46 </E>
<E ID="79"> 46 39 </E>
<E ID="80"> 46 47 </E>
<E ID="81"> 47 40 </E>
<E ID="82"> 47 48 </E>
<E ID="83"> 48 41 </E>
<E ID="84"> 42 49 </E>
<E ID="85"> 49 50 </E>
<E ID="86"> 50 43 </E>
<E ID="87"> 50 51 </E>
<E ID="88"> 51 44 </E>
<E ID="89"> 51 52 </E>
<E ID="90"> 52 45 </E>
<E ID="91"> 52 53 </E>
<E ID="92"> 53 46 </E>
<E ID="93"> 53 54 </E>
<E ID="94"> 54 47 </E>
<E ID="95"> 54 55 </E>
<E ID="96"> 55 48 </E>
<E ID="97"> 49 56 </E>
<E ID="98"> 57 56 </E>
<E ID="99"> 57 50 </E>
<E ID="100"> 58 57 </E>
<E ID="101"> 58 51 </E>
<E ID="102"> 59 58 </E>
<E ID="103"> 59 52 </E>
<E ID="104"> 60 59 </E>
<E ID="105"> 60 53 </E>
<E ID="106"> 61 60 </E>
<E ID="107"> 61 54 </E>
<E ID="108"> 62 61 </E>
<E ID="109"> 62 55 </E>
</EDGE>
<ELEMENT>
<Q ID="0"> 0 1 2 3 </Q>
<Q ID="1"> 2 4 5 6 </Q>
<Q ID="2"> 5 7 8 9 </Q>
<Q ID="3"> 8 10 11 12 </Q>
<Q ID="4"> 11 13 14 15 </Q>
<Q ID="5"> 14 16 17 18 </Q>
<Q ID="6"> 19 20 21 1 </Q>
<Q ID="7"> 21 22 23 4 </Q>
<Q ID="8"> 23 24 25 7 </Q>
<Q ID="9"> 25 26 27 10 </Q>
<Q ID="10"> 27 28 29 13 </Q>
<Q ID="11"> 29 30 31 16 </Q>
<Q ID="12"> 32 33 34 20 </Q>
<Q ID="13"> 34 35 36 22 </Q>
<Q ID="14"> 36 37 38 24 </Q>
<Q ID="15"> 38 39 40 26 </Q>
<Q ID="16"> 40 41 42 28 </Q>
<Q ID="17"> 42 43 44 30 </Q>
<Q ID="18"> 45 46 47 33 </Q>
<Q ID="19"> 47 48 49 35 </Q>
<Q ID="20"> 49 50 51 37 </Q>
<Q ID="21"> 51 52 53 39 </Q>
<Q ID="22"> 53 54 55 41 </Q>
<Q ID="23"> 55 56 57 43 </Q>
<Q ID="24"> 58 59 60 46 </Q>
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<Q ID="32"> 75 76 77 63 </Q>
<Q ID="33"> 77 78 79 65 </Q>
<Q ID="34"> 79 80 81 67 </Q>
<Q ID="35"> 81 82 83 69 </Q>
<Q ID="36"> 84 85 86 72 </Q>
<Q ID="37"> 86 87 88 74 </Q>
<Q ID="38"> 88 89 90 76 </Q>
<Q ID="39"> 90 91 92 78 </Q>
<Q ID="40"> 92 93 94 80 </Q>
<Q ID="41"> 94 95 96 82 </Q>
<Q ID="42"> 97 98 99 85 </Q>
<Q ID="43"> 99 100 101 87 </Q>
<Q ID="44"> 101 102 103 89 </Q>
<Q ID="45"> 103 104 105 91 </Q>
<Q ID="46"> 105 106 107 93 </Q>
<Q ID="47"> 107 108 109 95 </Q>
</ELEMENT>
<COMPOSITE>
<C ID="0"> Q[0-47] </C>
<C ID="1"> E[17,31,44,57,70,83,96,109,0,19,32,45,58,71,84,97] </C> //wall
<C ID="2"> E[3,6,9,12,15,18] </C>//inflow
<C ID="3"> E[98,100,102,104,106,108] </C> //outflow
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" NUMMODES="11" TYPE="MODIFIED" />
</EXPANSIONS>
</NEKTAR>
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Point(1) = {3.141592653589793, -1, 0, 1e+22};
Point(2) = {3.141592653589793, 1, 0, 1e+22};
Point(3) = {-3.141592653589793, 1, 0, 1e+22};
Point(4) = {-3.141592653589793, -1, 0, 1e+22};
Line(1) = {4, 1};
Line(2) = {1, 2};
Line(3) = {2, 3};
Line(4) = {3, 4};
Line Loop(5) = {2, 3, 4, 1};
Plane Surface(6) = {5};
Transfinite Line {1, 3} = 9 Using Progression 1;
Transfinite Line {4, 2} = 7 Using Bump 0.2;
Transfinite Surface{6};
Recombine Surface {6};
Physical Surface(10) = {6};
Physical Line(7) = {1, 3};
Physical Line(8) = {4};
Physical Line(9) = {2};
$MeshFormat
2.1 0 8
$EndMeshFormat
$Nodes
63
1 3.141592653589793 -1 0
2 3.141592653589793 1 0
3 -3.141592653589793 1 0
4 -3.141592653589793 -1 0
5 -2.356194490194426 -1 0
6 -1.57079632679906 -1 0
7 -0.7853981634023053 -1 0
8 -5.551115123125783e-12 -1 0
9 0.7853981633925913 -1 0
10 1.570796326790734 -1 0
11 2.356194490190263 -1 0
12 3.141592653589793 -0.8333332733409333 0
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<E ID="54"> 32 33 </E>
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<E ID="57"> 34 27 </E>
<E ID="58"> 28 35 </E>
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<E ID="64"> 38 31 </E>
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<E ID="105"> 60 53 </E>
<E ID="106"> 61 60 </E>
<E ID="107"> 61 54 </E>
<E ID="108"> 62 61 </E>
<E ID="109"> 62 55 </E>
</EDGE>
<ELEMENT>
<Q ID="0"> 0 1 2 3 </Q>
<Q ID="1"> 2 4 5 6 </Q>
<Q ID="2"> 5 7 8 9 </Q>
<Q ID="3"> 8 10 11 12 </Q>
<Q ID="4"> 11 13 14 15 </Q>
<Q ID="5"> 14 16 17 18 </Q>
<Q ID="6"> 19 20 21 1 </Q>
<Q ID="7"> 21 22 23 4 </Q>
<Q ID="8"> 23 24 25 7 </Q>
<Q ID="9"> 25 26 27 10 </Q>
<Q ID="10"> 27 28 29 13 </Q>
<Q ID="11"> 29 30 31 16 </Q>
<Q ID="12"> 32 33 34 20 </Q>
<Q ID="13"> 34 35 36 22 </Q>
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<Q ID="15"> 38 39 40 26 </Q>
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<Q ID="20"> 49 50 51 37 </Q>
<Q ID="21"> 51 52 53 39 </Q>
<Q ID="22"> 53 54 55 41 </Q>
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<Q ID="25"> 60 61 62 48 </Q>
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<Q ID="27"> 64 65 66 52 </Q>
<Q ID="28"> 66 67 68 54 </Q>
<Q ID="29"> 68 69 70 56 </Q>
<Q ID="30"> 71 72 73 59 </Q>
<Q ID="31"> 73 74 75 61 </Q>
<Q ID="32"> 75 76 77 63 </Q>
<Q ID="33"> 77 78 79 65 </Q>
<Q ID="34"> 79 80 81 67 </Q>
<Q ID="35"> 81 82 83 69 </Q>
<Q ID="36"> 84 85 86 72 </Q>
<Q ID="37"> 86 87 88 74 </Q>
<Q ID="38"> 88 89 90 76 </Q>
<Q ID="39"> 90 91 92 78 </Q>
<Q ID="40"> 92 93 94 80 </Q>
<Q ID="41"> 94 95 96 82 </Q>
<Q ID="42"> 97 98 99 85 </Q>
<Q ID="43"> 99 100 101 87 </Q>
<Q ID="44"> 101 102 103 89 </Q>
<Q ID="45"> 103 104 105 91 </Q>
<Q ID="46"> 105 106 107 93 </Q>
<Q ID="47"> 107 108 109 95 </Q>
</ELEMENT>
<COMPOSITE>
<C ID="0"> Q[0-47] </C>
<C ID="1"> E[17,31,44,57,70,83,96,109,0,19,32,45,58,71,84,97] </C> //wall
<C ID="2"> E[3,6,9,12,15,18] </C>//inflow
<C ID="3"> E[98,100,102,104,106,108] </C> //outflow
</COMPOSITE>
<DOMAIN> C[0] </DOMAIN>
</GEOMETRY>
<EXPANSIONS>
<E COMPOSITE="C[0]" NUMMODES="11" FIELDS="u,v" TYPE="GLL_LAGRANGE" />
</EXPANSIONS>
<CONDITIONS>
<SOLVERINFO>
<I PROPERTY="SolverType" VALUE="......"/>
<I PROPERTY="EQTYPE" VALUE="......"/>
<I PROPERTY="EvolutionOperator" VALUE="Direct" />
<I PROPERTY="Projection" VALUE="Galerkin"/>
<I PROPERTY="TimeIntegrationMethod" VALUE="IMEXOrder1"/>
<I PROPERTY="Driver" VALUE="...."/>
<I PROPERTY="InitialVector" VALUE="Random"/>
<I PROPERTY="ArpackProblemType" VALUE="...."/>
</SOLVERINFO>
<PARAMETERS>
<P> TimeStep = 0.002 </P>
<P> NumSteps = 500 </P>
<P> IO_CheckSteps = 1000 </P>
<P> IO_InfoSteps = 20 </P>
<P> Re = 7500 </P>
<P> Kinvis = 1.0/Re </P>
<P> kdim = 16 </P>
<P> nev =2 </P>
</PARAMETERS>
<VARIABLES>
<V ID="0"> u </V>
<V ID="1"> v </V>
</VARIABLES>
<BOUNDARYREGIONS>
<B ID="0"> C[1] </B>
<B ID="1"> C[2] </B>
<B ID="2"> C[3] </B>
</BOUNDARYREGIONS>
<BOUNDARYCONDITIONS>
<REGION REF="0">
<D VAR="u" VALUE="0" />
<D VAR="v" VALUE="0" />
</REGION>
<REGION REF="1">
<P VAR="u" VALUE="[2]" />
<P VAR="v" VALUE="[2]" />
</REGION>
<REGION REF="2">
<P VAR="u" VALUE="[1]" />
<P VAR="v" VALUE="[1]" />
</REGION>
</BOUNDARYCONDITIONS>
<FUNCTION NAME="ExactSolution">
<E VAR="u" VALUE="-y*y+1" />
<E VAR="v" VALUE="0" />
</FUNCTION>
</CONDITIONS>
</NEKTAR>
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