Functions/Subroutines
subroutine	lcpfct (RHOO, RHON, I1, IN, SOURCE)
	Originated: J.P. Boris Code 4400, NRL Feb 1987 Modified: Laboratory for Computational Physics & Fluid Dynamics Contact: J.P. Boris, J.H. Gardner, A.M. Landsberg, or E.S. Oran. More...

subroutine	makegrid (RADHO, RADHN, I1, INP, mode, RLN_OUT, VOLO, VOLN, SURFO, SURFN, coef_geom, mat_filtre)
	Description: This Subroutine initializes geometry variables and coefficients. It should be called first to initialize the grid. The grid must be defined for all of the grid interfaces from I1 to INP. Subsequent calls to VELOCITY and LCPFCT can work on only portions of the grid, however, to perform restricted integrations on separate line segments. More...

subroutine	velocity (UH, I1, INP, DT, ADVEC)
	Description: This subroutine calculates all velocity-dependent coefficients for the LCPFCT and CNVFCT routines. This routine must be called before either LCPFCT or CNVFCT is called. MAKEGRID must be called earlier to set grid and geometry data used here. More...

subroutine	sources (I1, IN, DT, MODE, C, D, SOURCE)
	Description: This subroutine computes different source terms. More...

real *8 function, dimension(size(var_cell)+1)	grid (itp, var_cell, pos2grid, sigma)
	Compute var_grid on grid cell interface from a variable given at cell (var_cell). More...

real *8 function, dimension(i1:in)	limite_gradln (I1, IN, D, G, Tp)
	Gradient grad(D) computation and limitation with Lo and given G and Tp. More...

real *8 function, dimension(size(src_in))	limite_src (I1, IN, SRC_in, G, Tp, Cij)

Detailed Description

Author

Date: 01.01.2011

Function/Subroutine Documentation

real*8 function, dimension(size(var_cell)+1) grid	(	integer, intent(in)	itp,
		real*8, dimension(:), intent(in)	var_cell,
		real*8, dimension(:), intent(in)	pos2grid,
		real*8, optional	sigma
	)

Compute var_grid on grid cell interface from a variable given at cell (var_cell).

Author: For i=2..N:
$\begin{equation}vgrid_i = pos2grid_i*vcell_i+(1-pos2grid_i)*vcell_{i-1}\end{equation}$

For i=1 or N+1:

Mode itp=1: for all variable except N and ln(N).
$\begin{eqnarray*} vgrid_1 &=& vcell_1 + \alpha (vcell_1 - vgrid_2)\\\ vgrid_{N+1} &=& vcell_N + \alpha (vcell_N - vgrid_N)\\\ vgrid_1.vcell_1 \ge 0 && vgrid_{N+1}.vcell_N \ge 0 \end{eqnarray*}$
Mode itp=2: for N.
$\begin{eqnarray*} vgrid_1 &=& vcell_1 + \alpha.max(0,(vcell_1 - vgrid_2))\\\ vgrid_{N+1} &=& coefrho.vcell_N \end{eqnarray*}$
Mode itp=3: for ln(N).
$\begin{eqnarray*} vgrid_1 &=& vcell_1 + \alpha.max(0,(vcell_1 - vgrid_2))\\\ vgrid_{N+1} &=& ln(coefrho) + vcell_N \end{eqnarray*}$

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subroutine lcpfct	(	real*8, dimension(:)	RHOO,
		real*8, dimension(:)	RHON,
		integer	I1,
		integer	IN,
		real*8, dimension(:)	SOURCE
	)

Originated: J.P. Boris Code 4400, NRL Feb 1987 Modified: Laboratory for Computational Physics & Fluid Dynamics Contact: J.P. Boris, J.H. Gardner, A.M. Landsberg, or E.S. Oran.

Author: Description: This routine solves generalized continuity equations of the form dRHO/dt = -div (RHO*V) + SOURCES in the user's choice of Cartesian, cylindrical, or spherical coordinate systems. A facility is included to allow definition of other coordinates. The grid can be Eulerian, sliding rezone, or Lagrangian and can be arbitrarily spaced. The algorithm is a low-phase-error FCT algorithm, vectorized and optimized for a combination of speed and flexibility. A complete description appears in the NRL Memorandum Report (1992), "LCPFCT - A Flux-Corrected Transport Algorithm For Solving Generalized Continuity Equations".

Arguments: RHOO Real Array grid point densities at start of step I RHON Real Array grid point densities at end of step O I1 Integer first grid point of integration I IN Integer last grid point of intergration I SRHO1 Real Array boundary guard cell factor at cell I1+1 I VRHO1 Real Array boundary value added to guard cell I1-1 I SRHON Real Array boundary guard cell factor at cell IN+1 I VRHON Real Array boundary value added to guard cell IN+1 I PBC Logical periodic boundaries if PBC = .true. I

In this routine the last interface at RADHN(INP) is the outer boundary of the last cell indexed IN. The first interface at RADHN(I1) is the outer boundary of the integration domain before the first cell indexed I1.

Language and Limitations: LCPFCT is a package of FORTRAN 77 sub- routines written in single precision (64 bits CRAY). The parameter NPT is used to establish the internal FCT array dimensions at the maximum size expected. Thus NPT = 500 means that continuity equa- tions for systems up to 200 cells long in one direction can be integrated. Underflows can occur when the function being trans- ported has a region of zeroes. The calculations misconserve by one or two bits per cycle. Relative phase and amplitude errors (for smooth functions) are typically a few percent for character- istic lengths of 1 - 2 cells (wavelengths of order 10 cells). The jump conditions for shocks are generally accurate to better than 1 percent. Common blocks are used to transmit all data between the subroutines in the LCPFCT package.

Auxiliary Subroutines: CNVFCT, CONSERVE, COPYGRID, MAKEGRID, NEW_GRID, RESIDIFF, SET_GRID, SOURCES, VELOCITY, ZERODIFF, and ZEROFLUX. The detailed documentation report provided (or the listing below) explains the definitions and use of the arguments to these other subroutines making up the LCPFCT package. These routines are not called from LCPFCT itself but are controlled by calls from the user. Subroutines MAKEGRID, VELOCITY and SOURCES in this package must first be called to set the grid geometry, velocity-dependent flux and diffusion coefficients, and external source arrays used by LCPFCT. The other subroutines may be called to perform other functions such as to modify boundary conditions, to perform special grid operations, or compute conservation sums.

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real*8 function, dimension(i1:in) limite_gradln	(	integer, intent(in)	I1,
		integer, intent(in)	IN,
		real*8, dimension(:), intent(in)	D,
		real*8, dimension(:), intent(in)	G,
		real*8, dimension(:), intent(in)	Tp
	)

Gradient grad(D) computation and limitation with Lo and given G and Tp.

Author

Parameters

I1.	Integer. First cell of the grid
IN.	Integer. Last cell of the grid
D.	Real Array(NPT). Array of variable to be derived.
G.	Real Array(NPT). Array of gravity value.
D.	Real Array(NPT). Array of parallel temperature.

Returns

GRD. Real Array(I1:IN). Limited gradient of D.

$\begin{equation} \nabla D^i = AR^i(D^{i+1}-D^i) \end{equation}$

$\begin{eqnarray*} \nabla D &<& \left| \frac{Lo.G}{T_p} \right| \hspace{10mm} if \hspace{1mm} G.\nabla D < 0\\ \nabla D &<& 10\left| \frac{Lo.G}{T_p} \right| \hspace{10mm} if \hspace{1mm} G.\nabla D > 0 \end{eqnarray*}$

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real*8 function, dimension(size(src_in)) limite_src	(	integer	I1,
		integer	IN,
		real*8, dimension(:)	SRC_in,
		real*8, dimension(:)	G,
		real*8, dimension(:)	Tp,
		real*8	Cij
	)

Author

subroutine makegrid	(	real*8, dimension(:)	RADHO,
		real*8, dimension(:)	RADHN,
		integer	I1,
		integer	INP,
		integer	mode,
		real*8, dimension(:)	RLN_OUT,
		real*8, dimension(:), optional	VOLO,
		real*8, dimension(:), optional	VOLN,
		real*8, dimension(:), optional	SURFO,
		real*8, dimension(:), optional	SURFN,
		real*8, dimension(:), optional	coef_geom,
		real*8, dimension(:,:), optional	mat_filtre
	)

Description: This Subroutine initializes geometry variables and coefficients. It should be called first to initialize the grid. The grid must be defined for all of the grid interfaces from I1 to INP. Subsequent calls to VELOCITY and LCPFCT can work on only portions of the grid, however, to perform restricted integrations on separate line segments.

Author: Arguments: RADHO Real Array(INP) old cell interface positions I RADHN Real Array(INP) new cell interface positions I I1 Integer first cell interface I INP Integer last cell interface I ALPHA Integer = 1 for cartesian geometry I = 2 for cylindrical geometry I = 3 for spherical geometry I = 4 general geometry (user supplied) I

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subroutine sources	(	integer, intent(in)	I1,
		integer, intent(in)	IN,
		real*8, intent(in)	DT,
		integer, intent(in)	MODE,
		real*8, dimension(:), intent(in)	C,
		real*8, dimension(:), intent(in)	D,
		real*8, dimension(:), intent(out)	SOURCE
	)

Description: This subroutine computes different source terms.

Author

Parameters

I1.	Integer. First cell to be integrated
IN.	Integer. Last cell to be integrated
DT.	Real. Stepsize for the time integration
MODE.	Integer. 1. Adds +DIV(D) 2. Adds +CGRAD(D) 3. Adds +D to the sources. 4. Adds +DIV(D) from interface data 5. Adds +CGRAD(D) from interface data. $SOURCE^i =+ C^i.dt.AR^i\left(D^{i+1}-D^i\right)$ 6. Adds +CDIV(D) conservatively from interface data. $SOURCE^i =+ C^i.dt\left(AH^{i+1}D^{i+1}-AH^iD^i\right)$ 7. Adds +CGRAD(D) using limited GRAD(D) expression.
C.	Real Array(NPT). Array of source variables
D.	Real Array(NPT). Array of source variables

Returns: SOURCE. Real Array(NPT). Array of sources.

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subroutine velocity	(	real*8, dimension(:)	UH,
		integer	I1,
		integer	INP,
		real*8	DT,
		integer, optional	ADVEC
	)

Description: This subroutine calculates all velocity-dependent coefficients for the LCPFCT and CNVFCT routines. This routine must be called before either LCPFCT or CNVFCT is called. MAKEGRID must be called earlier to set grid and geometry data used here.

Author: Arguments: UH Real Array(NPT) flow velocity at cell interfaces I I1 Integer first cell interface of integration I INP Integer last cell interface = N + 1 I DT Real stepsize for the time integration I

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Functions/Subroutines

Detailed Description

Function/Subroutine Documentation