advpbv.F

subroutine advpbv (ba, hin, hout)

Description

The subroutine performs advection of any scalar variable in the $v$ (or $y$) direction by PPM (the piecewise parabolic method). This method ensures positivity and scalar conservation with a minimum of numerical diffusion. The routine is directionally split, first advecting in the $v$ direction, then in the vertical. The routine returns new values of the scalar at the original $\sigma$ or $s$ levels and a new total depth. The vertical advection is performed by considering control volumes, which are remapped on to the original $\sigma$ or $s$ levels. An alternative (`new') method is chosen if the CFL condition is violated in the vertical; this method allows any value of vertical Courant number.

When preceded by advpbu, which advects in the $u$ (or $x$) direction, followed by a vertical advection, a complete directionally split advection cycle has been performed, and a final total depth has been returned. Since advection is performed on the longer baroclinic time step DT, the final depth, which is given by the volume fluxes, should be equal to the final depth over the corresponding number of barotropic time steps. This is ensured by making the volume fluxes used equal to the sum of barotropic volume fluxes. The routine advect_sca controls the order of advection in the two horizontal directions: this may alternate on successive time steps. A laplacian horizontal diffusive flux can be included at the intermediate stage, with either a fixed or Smagorinsky diffusity (see htmlrefhorizdiffusivityhorizdiffusivity)

Numerical Equations

See advpbu

Subroutine Arguments

ba value of scalar variable, returns new value

hin initial depth

hout final depth

Local variables

b2 intermediate value of advected scalar

bl,br value of parabola at left and right of interval

d2b value of $\delta^2 b$

dba difference of $ba$

dfl2 flux difference

dmb value of $\delta_m b$

ds2 difference between intermediate sigma levels

dsig difference between intermediate and original sigma levels

fba scalar flux

fvv volume flux

sigo3 intermediate sigma levels

i,j,k,icg,jcg,jlb,jub grid indices

tagba,tagdba,tagdmb,tagd2b,tagu,tagh,tagbr,tagbl ,tagfu,tagfba integers used in Exch3DS and Exch3DR routines

a1,a2,a3,b6,bdl,bdr,delb,delb2,delb6 variables used in parabola calculations (see above description)

eti,ett variables used in steepening option

e1,e2,eps parameters used in steepening option

aip mask variable used in flux calculations

rcdal length of grid box side in lat-long coordinates

xdb used in setting parabolas in vertical with uneven grid spacing

xi length over which parabola is integrated to give flux

advmask logical variable based on mask

ivi 0 or 1 whether or not vertical Courant number is $< 1$

k1,k0,ka,kb,kc vertical indices used in `new' vertical advection scheme

dsi sigma coordinate differences used in `new' vertical advection scheme

baa,bab,bat variables used in `new' vertical advection scheme

inv3,inv6 1/3,1/6

HD imposed horizontal diffusive flux

pri turbulent Prandlt number (inverse)

Logical units

Only used in debugging option.

Global variables changed

none

Order of Things

1. Calculate parabolas in horizontal
2. Steepen (optional) and monotonise parabolas
3. Calculate horizontal fluxes and intermediate $\sigma$ levels
4. Calculate parabolas in vertical
5. Steepen (optional) and monotonise parabolas
6. Calculate intermediate value of ba with horizontal diffusion if required.
7. Redistribute on to original $\sigma$ or $s$ levels

Calls

Exch3DS, Exch3DR

MPI_GatherV

Called By

advect_sca

Options - Logical

adv_bc advective boundary conditions

Options - Compiler

DEBUG, DEBUG_ADV outputs debugging information

TIMING_ADV timing of advection routines

SCOORD $\sigma$-level spacing varies horizontally

NOSTEEP turns off steepening during horizontal calculation

NOSTEEPZ turns off steepening during vertical calculation

HORIZ_DIF_TS Horizontal diffusion of T and S on $\sigma$-levels

Known Issues

Limitations of directional splitting