programing_guide:available_constructions_of

Focus Manuals: Programing Guide: Building matrices and vectors: Available construction of Vectors

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FORMULs of SUBROUTINE VECTOR

MASMAS

FORMUL = 'MASMAS '

(subroutines with names which start with VC00)

Integrals of the bases, or product of a mass matrix by a vector with the value of 1 everywhere.

$VEC(i) = XMUL \int_\Omega \psi_i \,d\Omega$

MASVEC

FORMUL = 'MASVEC '

(subroutines with names which start with VC01)

Product of a mass matrix by a vector F.

$VEC(i) = XMUL \int_\Omega F \psi_i \,d\Omega$

SUPG

FORMUL = 'SUPG '

(subroutines with names which start with VC03)

$VEC(i) = XMUL \int_\Omega \big( \overrightarrow{K}.\overrightarrow{grad}(\psi_i) \overrightarrow{U}.\overrightarrow{grad}(F) \big) \,d\Omega$

$\overrightarrow{K}$ is a vector with the components G and H. (this would have to be modified in dimension 3).
$\overrightarrow{U}$ is a vector with the components U, V and W.

VGRADP and VGRADP2

FORMUL = 'VGRADP ' or 'VGRADP2 ' (used in 3D only)

(subroutines with names which start with VC04)

$VEC(i) = XMUL \int_\Omega \overrightarrow{U_2_D}.\overrightarrow{grad}(\psi_i) \,d\Omega$

$\overrightarrow{U_2_D}$ is a vector with the components U and V.

VGRADP is the same formula, with corrections when the generalised sigma transformation is used.

FLUBOR

FORMUL = 'FLUBOR '

(subroutines with names which start with VC05)

$VEC(i) = XMUL \int_\Gamma \big( \psi_i \overrightarrow{U}.\overrightarrow{n} \big) \,d\Gamma$

$\overrightarrow{U}$ is a vector with the components U, V and W.
$\overrightarrow{n}$ is the normal outer vector.

FLUBOR2

FORMUL = 'FLUBOR2 '

In 3D only, FLUBOR2 is like FLUBOR, but in the case of a generalised sigma transformation.

VGRADF

FORMUL = 'VGRADF '

(subroutines with names which start with VC08)

$VEC(i) = XMUL \int_\Omega \big( \psi_j \overrightarrow{U}.\overrightarrow{grad}(F) \big) \,d\Omega$

$\overrightarrow{U}$ is a vector with the components U, V and W.

QGRADF

FORMUL = 'QGRADF '

(subroutines with names which start with VC09)

$VEC(i) = XMUL \int_\Omega \big( \psi_i G \overrightarrow{U}.\overrightarrow{grad}(F) \big) \,d\Omega$

$\overrightarrow{U}$ is a vector with the components U, V and W.

FLUBDF

FORMUL = 'FLUBDF '

(subroutines with names which start with VC10)

$VEC(i) = XMUL \int_\Gamma \big( \psi_i F \overrightarrow{U}.\overrightarrow{n} \big) \,d\Gamma$

$\overrightarrow{U}$ is a vector with the components U, V and W.
$\overrightarrow{n}$ is the normal outer vector.

GGRADF

FORMUL = 'GGRADF X'

(subroutines with names which start with VC11)

$VEC(i) = XMUL \int_\Omega \big( \psi_j G \overrightarrow{grad}(F) \big) \,d\Omega$

Beware the minus sign !!!!

If FORMUL(16:16) is equal to 'Y' or 'Z' instead of 'X' , the derivatives will be obtained according to y or z.

GRADF

FORMUL = 'GRADF X'

(subroutines with names which start with VC13)

$VEC(i) = XMUL \int_\Omega \big( \psi_i \overrightarrow{grad}(F) \big) \,d\Omega$

If FORMUL(16:16) is equal to 'Y' or 'Z' instead of 'X' , the derivatives will be obtained according to y or z.

In 3 dimensions, variants are available:

GRADF(X,Y) X and GRADF(X,Y) Y will consider only the gradient of a function

which does not depend on 'Z'.

GRADF2 will take care of hydrostatic inconsistencies.

PRODF

FORMUL = 'PRODF'

(subroutines with names which start with VC14)

$VEC(i) = XMUL \int_\Omega \psi_i F \big( 2(\frac{\partial U}{\partial x})^2 + 2(\frac{\partial V}{\partial x})^2 + (\frac{\partial U}{\partial y}+\frac{\partial V}{\partial x})^2 \big) \,d\Omega$

This vector is used in the calculation of the turbulent production with the model k-epsilon.

DIVQ

FORMUL = 'DIVQ '

(subroutines with names which start with VC15)

$VEC(i) = XMUL \int_\Omega \big( \psi_i div(F \overrightarrow{U} \big) \,d\Omega$

$\overrightarrow{U}$ is a vector with the components U, V and W.

SUPGDIVU

FORMUL = 'SUPGDIVU '

(subroutines with names which start with VC16)

$VEC(i) = XMUL \int_\Omega \big( \overrightarrow{K} \overrightarrow{grad}(\psi_i).div(\overrightarrow{U}) \big) \,d\Omega$

$\overrightarrow{U}$ is a vector with the components U, V and W.
$\overrightarrow{K}$ is a vector with the components F, G and H.

FLUDIF

FORMUL = 'FLUDIF '

(subroutines with names which start with VC17)

$VEC(i) = XMUL \int_\Omega \big( \psi_i U \overrightarrow{grad}(F).\overrightarrow{n} \big) \,d\Omega$

This is not currently used nor implemented.

VGRADF2

FORMUL = 'VGRADF2 '

(subroutines with names which start with VC18)

$VEC(i) = XMUL \int_\Omega \big( \psi_i U \overrightarrow{grad}(F) \big) \,d\Omega$

This is specifically for 3D computations with prisms, and unlike VGRADF, the test function $\psi_i$ is here a 2-dimensional test function (no dependency on z). This is used by Telemac-3D in subroutine WSTARW.

HUGRADP

FORMUL = 'HUGRADP '

(subroutines with names which start with VC19)

$VEC(i) = XMUL \int_\Omega \big( F \overrightarrow{U} \overrightarrow{grad}(\psi_i) \big) \,d\Omega$

This is used in 2D, mostly for computing fluxes. H in HUGRADP stands for the depth denoted h, which can be misleading as it does not refer to the function H which is an argument of subroutine VC19AA. A variant HUGRADP2 exists, in this case the velocity is not only $\overrightarrow{U}$ of components (U,V), but $U + G \overrightarrow{grad}(H)$ . This is a way of treating the gradient of the free surface elevation as a piecewise constant function, which it is in reality when the depth is linear.

SUBROUTINE BY NAMES

The existing subroutines building vectors in version 6.+ are the following, their function can be deduced from the explanations above:

vc00aa.f vc00bb.f vc00cc.f vc00pp.f vc00pp2.f
vc00ft.f vc00ff.f vc00tt.f vc01aa.f vc01bb.f
vc01ff.f vc01ft.f vc01oo.f vc01pp.f vc01tt.f
vc01tt0.f vc03aa.f vc03bb.f vc04aa.f vc04pp.f
vc05oo.f vc05aa.f vc04tt.f vc05ff.f vc05ft.f
vc08aa.f vc08bb.f vc08cc.f vc08pp.f vc08tt.f
vc09aa.f vc10oo.f vc11aa.f vc11aa2.f vc11bb.f
vc11pp.f vc11tt.f vc11tt0.f vc13aa.f vc13bb.f
vc13cc.f vc13pp.f vc13pp2.f vc13tt.f vc14aa.f
vc15aa.f vc16aa.f vc18pp.f vc19aa.f