Changeset 11512 for NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_conservation.tex

Timestamp:

2019-09-09T12:05:20+02:00 (5 years ago)

Author:

smasson

Message:

dev_r10984_HPC-13 : merge with trunk@11511, see #2285

File:

• NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_conservation.tex (modified) (5 diffs)

NEMO/branches/2019/dev_r10984_HPC-13_IRRMANN_BDY_optimization/doc/latex/NEMO/subfiles/chap_conservation.tex

@@ -8 +8 @@
 \chapter{Invariants of the Primitive Equations}
 \label{chap:Invariant}
-\minitoc
+\chaptertoc
 
 The continuous equations of motion have many analytic properties.
@@ -35 +35 @@
 The alternative is to use diffusive schemes such as upstream or flux corrected schemes.
 This last option was rejected because we prefer a complete handling of the model diffusion,
-\ie of the model physics rather than letting the advective scheme produces its own implicit diffusion without
+\ie\ of the model physics rather than letting the advective scheme produces its own implicit diffusion without
 controlling the space and time structure of this implicit diffusion.
 Note that in some very specific cases as passive tracer studies, the positivity of the advective scheme is required.
@@ -122 +122 @@
 This properties is satisfied locally with the choice of discretization we have made (property (II.1.9)~).
 In addition, when the equation of state is linear
-(\ie when an advective-diffusive equation for density can be derived from those of temperature and salinity)
+(\ie\ when an advective-diffusive equation for density can be derived from those of temperature and salinity)
 the change of horizontal kinetic energy due to the work of pressure forces is balanced by the change of
 potential energy due to buoyancy forces:
@@ -283 +283 @@
 In discrete form, all these properties are satisfied in $z$-coordinate (see Appendix C).
 In $s$-coordinates, only first order properties can be demonstrated,
-\ie the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence.
+\ie\ the vertical momentum physics conserve momentum, potential vorticity, and horizontal divergence.
 
 % -------------------------------------------------------------------------------------------------------------
@@ -294 +294 @@
 the heat and salt contents are conserved (equations in flux form, second order centred finite differences).
 As a form flux is used to compute the temperature and salinity,
-the quadratic form of these quantities (\ie their variance) globally tends to diminish.
+the quadratic form of these quantities (\ie\ their variance) globally tends to diminish.
 As for the advective term, there is generally no strict conservation of mass even if,
 in practice, the mass is conserved with a very good accuracy.