GetLprimeStokes

PURPOSE ^

GETLPRIMESTOKES - compute Lprime matrix for stokes diagnostic

SYNOPSIS ^

function Lprime=GetLprimeStokes(triaelem,xyz_list,gauss_coord_tria,gauss_coord_penta)

DESCRIPTION ^

GETLPRIMESTOKES - compute Lprime matrix for stokes diagnostic

   Compute Lprime  matrix. Lprime=[Lp1 Lp2 Lp3] where Lpi is square and of size numdof. 
   For grid i, Lpi can be expressed in the basic coordinate system by:
   Lpi_basic=[ h    0    0   0]
             [ 0    h    0   0]
             [ h    0    0   0]
             [ 0    h    0   0]
             [ 0    0    h   0]
             [ 0    0    h   0]
             [ 0    0  dh/dz 0]
             [ 0    0  dh/dz 0]
             [ 0    0  dh/dz 0]
             [dh/dz 0  dh/dx 0]
             [ 0 dh/dz dh/dy 0]
             [ 0    0    0   h]
             [ 0    0    0   h]
             [ 0    0    0   h]
   where h is the interpolation function for grid i.

   Usage:
      Lprime=GetLprimeStokes(triaelem,xyz_list,gauss_coord_tria,gauss_coord_penta)

   See also GETLSTOKES, GETL, CREATEKMATRIX

CROSS-REFERENCE INFORMATION ^

This function calls: This function is called by:

SOURCE CODE ^

0001 function Lprime=GetLprimeStokes(triaelem,xyz_list,gauss_coord_tria,gauss_coord_penta)
0002 %GETLPRIMESTOKES - compute Lprime matrix for stokes diagnostic
0003 %
0004 %   Compute Lprime  matrix. Lprime=[Lp1 Lp2 Lp3] where Lpi is square and of size numdof.
0005 %   For grid i, Lpi can be expressed in the basic coordinate system by:
0006 %   Lpi_basic=[ h    0    0   0]
0007 %             [ 0    h    0   0]
0008 %             [ h    0    0   0]
0009 %             [ 0    h    0   0]
0010 %             [ 0    0    h   0]
0011 %             [ 0    0    h   0]
0012 %             [ 0    0  dh/dz 0]
0013 %             [ 0    0  dh/dz 0]
0014 %             [ 0    0  dh/dz 0]
0015 %             [dh/dz 0  dh/dx 0]
0016 %             [ 0 dh/dz dh/dy 0]
0017 %             [ 0    0    0   h]
0018 %             [ 0    0    0   h]
0019 %             [ 0    0    0   h]
0020 %   where h is the interpolation function for grid i.
0021 %
0022 %   Usage:
0023 %      Lprime=GetLprimeStokes(triaelem,xyz_list,gauss_coord_tria,gauss_coord_penta)
0024 %
0025 %   See also GETLSTOKES, GETL, CREATEKMATRIX
0026 
0027 numdof=4;
0028 num_grids=3;
0029 
0030 %Get l1l2l3 in basic coordinate system:
0031 l1l2l3=GetNodalFunctions(triaelem,gauss_coord_tria);
0032 dh1dh6=GetNodalFunctionsDerivativesBasic(pentaelem,xyz_list,gauss_coord_penta);
0033 
0034 %Build Lprime:
0035 Lprime=zeros(12,numdof*num_grids);
0036 
0037 for i=1:num_grids,
0038     Lprime(1,numdof*(i-1)+1)=l1l2l3(i); 
0039     Lprime(2,numdof*(i-1)+2)=l1l2l3(i);
0040     Lprime(3,numdof*(i-1)+1)=l1l2l3(i); 
0041     Lprime(4,numdof*(i-1)+2)=l1l2l3(i); 
0042     Lprime(5,numdof*(i-1)+3)=l1l2l3(i); 
0043     Lprime(6,numdof*(i-1)+3)=l1l2l3(i); 
0044     Lprime(7,numdof*(i-1)+3)=dh1dh6(3,i); 
0045     Lprime(8,numdof*(i-1)+3)=dh1dh6(3,i); 
0046     Lprime(9,numdof*(i-1)+3)=dh1dh6(3,i); 
0047     Lprime(10,numdof*(i-1)+3)=dh1dh6(1,i); 
0048     Lprime(10,numdof*(i-1)+1)=dh1dh6(3,i); 
0049     Lprime(11,numdof*(i-1)+3)=dh1dh6(2,i); 
0050     Lprime(11,numdof*(i-1)+2)=dh1dh6(3,i); 
0051     Lprime(12,numdof*(i-1)+4)=l1l2l3(i); 
0052     Lprime(13,numdof*(i-1)+4)=l1l2l3(i); 
0053     Lprime(14,numdof*(i-1)+4)=l1l2l3(i); 
0054     
0055 %other terms are 0
0056 end

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