📄 cfd recipes chapter 9.mht
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Subject: CFD Recipes: Chapter 9
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<HTML><HEAD><TITLE>CFD Recipes: Chapter 9</TITLE>
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<DIV align=3Dcenter><IMG height=3D42 alt=3D"Cambridge University Press"=20
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<BR><IMG=20
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<TD vAlign=3Dtop align=3Dright><FONT size=3D+0><A=20
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<P><A href=3D"http://capella.colorado.edu/~laney/toc.htm">Table of =
Contents</A>=20
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href=3D"http://capella.colorado.edu/~laney/index.htm">Index</A>=20
<P><A =
href=3D"http://capella.colorado.edu/~laney/reviews.htm">Reviews</A>=20
<P><A =
href=3D"http://capella.colorado.edu/~laney/software.htm">Software</A>=20
<P><A =
href=3D"http://capella.colorado.edu/~laney/hwsolns.htm">Solutions to=20
Problems</A>=20
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href=3D"http://capella.colorado.edu/~laney/additional.htm">Additional=20
Material</A>=20
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of Interest</A>=20
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Sites of=20
Interest</A>=20
<P><A href=3D"http://capella.colorado.edu/~laney/author.htm">About =
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Author</A>=20
<P><A =
href=3D"http://capella.colorado.edu/~laney/purchase.htm">Purchase the=20
Book</A> </FONT></P></TD>
<TD vAlign=3Dtop>
<BLOCKQUOTE>
<H1>Software for <I>Computational Gasdynamics</I></H1><BR><IMG=20
=
src=3D"http://capella.colorado.edu/~laney/graphics/cfdrecipes.jpg"=20
border=3D0> <BR><BR>
<HR>
<H2>Chapter 9. Piecewise-Polynomial Reconstruction</H2>
<HR>
<BR>
<TABLE cellSpacing=3D0 cellPadding=3D5 border=3D0>
<TBODY>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch9soft/spline.f">Cubic=20
Splines</A></TD></TR>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch8soft/interp1.dat">Sample=20
Input File 1</A></TD></TR>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch8soft/interp2.dat">Sample=20
Input File 2</A></TD></TR></TBODY></TABLE>
<P>This code requires an ASCII input file interp.dat of the =
following=20
form:=20
<BLOCKQUOTE><I>N: Number of Spline Interpolation Points =
(Small)</I>
<P><I>First Sample (x1,y1)</I>
<P><I>Second Sample (x2,y2)</I>
<P>...
<P><I>Nth Sample (xN,yN)</I>
<P><I>N1: Number of Error Evaluation Points (Large)</I>
<P><I>First Sample (x1,y1)</I>
<P><I>Second Sample (x2,y2)</I>
<P>...
<P><I>N1th Sample (xN1,yN1)</I>
<P></P></BLOCKQUOTE>This code will produce two ASCII output =
files:=20
<UL>
<LI>spline.out. This contains the polynomial coefficients in =
Taylor=20
series form for each interval defined by the spline =
interpolation=20
points.=20
<LI>spline.plt. The spline evaluated at the error evaluation =
points.=20
</LI></UL>The book mentions splines but provides no details. =
Using the=20
above code, you can compare the performance of cubic splines to =
other=20
more exotic types of piecewise-polynomial reconstructions.
<P><BR>
<TABLE cellSpacing=3D0 cellPadding=3D5 border=3D0>
<TBODY>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch9soft/rp.f">Piecewise-Quadra=
tic=20
ENO Reconstruction (via the Primitive Function) =
</A></TD></TR>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch9soft/rd.f">Average-Quadrati=
c=20
ENO Reconstruction (via the Primitive =
Function)</A></TD></TR>
<TR>
<TD><A=20
=
href=3D"http://capella.colorado.edu/~laney/ch9soft/cell.dat">Sample=20
Input File</A></TD></TR></TBODY></TABLE>
<P>These codes require an ASCII input file cell.dat of the =
following=20
form:=20
<BLOCKQUOTE><I>N: Number of Cells (Small)</I>
<P><I>First Cell Edge (x1)</I>
<P><I>Second Cell Edge (x2)</I>
<P>...
<P><I>Nth Cell Edge (xN,yN)</I>
<P><I>N+1th Cell Edge (xN+1,yN+1)</I>
<P><I>First Cell-Integral Average (y1)</I>
<P><I>Second Cell-Integral Average (y2)</I>
<P>...
<P><I>Nth Cell-Intgeral Average (yN)</I>
<P><I>N1: Number of Error Evaluation Points (Large)</I>
<P><I>First Sample (x1,y1)</I>
<P><I>Second Sample (x2,y2)</I>
<P>...
<P><I>N1th Sample (xN1,yN1)</I>
<P></P></BLOCKQUOTE>These codes will produce a single ASCII =
output file=20
called rp.out or rd.out containing the reconstruction evaluated =
at the=20
error evaluation points.
<P>Using the sample input file, these codes will generate =
figures 9.7=20
and 9.8 in the book.=20
<P></P></BLOCKQUOTE></TD></TR></TBODY></TABLE><BR>
<DIV align=3Dcenter>[ <A=20
href=3D"http://capella.colorado.edu/~laney/booksoft.htm">Book Software =
Home</A> |=20
<A href=3D"http://capella.colorado.edu/~laney/ch4code.htm">Chapter 4</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch5code.htm">Chapter 5</A> | =
<BR><A=20
href=3D"http://capella.colorado.edu/~laney/ch8code.htm">Chapter 8</A> | =
<A=20
href=3D"http://capella.colorado.edu/~laney/ch11code.htm">Chapter 11</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch17code.htm">Chapter 17</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch18code.htm">Chapter 18</A> =
| <BR><A=20
href=3D"http://capella.colorado.edu/~laney/ch20code.htm">Chapter 20</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch21code.htm">Chapter 21</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch22code.htm">Chapter 22</A> =
| <A=20
href=3D"http://capella.colorado.edu/~laney/ch23code.htm">Chapter 23</A> =
]=20
</DIV><BR><BR>
<HR>
<FONT size=3D-1><I>© 2000, Culbert B. Laney </I> =
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