D A P H N I S
Depth-Averaged Plane Hydrotechnical Networks Integrated Simulation


The code DAPHNIS is intended do simulate both one- and two- dimensional
depth-averaged transient flow in domains of complex shape, such as
networks of channels, systems of channels and reservoirs, single or
coupled hydrotechnical objects.

Equations of the mathematical model of flow, namely the vertically averaged
Navier-Stokes equations:

   dH     d(hu)     d(hv)
   --  +  -----  +  -----  =  0 ,
   dt      dx        dy

   d(hu)     d(bhu^2+P)     d(bhuv)               dH
   -----  +  ----------  +  -------  +  gh( Sx +  -- ) =  n div Tx ,
    dt          dx            dy                  dx

   d(hv)     d(bhuv)     d(bhv^2+P)               dH
   -----  +  -------  +  ----------  +  gh( Sy +  -- ) =  n div Ty ,
    dt         dx            dy                   dy

include: advective terms, hydrostatic pressure term,
source term (including bed slope and Manning-Strickler
vertically averaged bottom stress effect), viscous term
in the form of Boussinesq's turbulent stress tensor with
constant vs. Kuipers' eddy viscosity approach.
Viscosity terms are optional.

The equations can be additionally averaged in the model
by introduction of rigid-lid cross-sectional assumption or
by total cross-sectional averaging of flow. They can also
be reduced to 1-D flow equations.

Boundary conditions support situations that commonly appear in 
real flow problems, including local stage and discharge time-dependent
conditions, nonlocal discharge conditions with flow redistribution rules,
over- and underflow weir-type conditions in all regimes of flow.
No assumptions are made about flow regime within the modelled domain.
Viscous flow can be modelled with several slip conditions.
No moving-boundary conditions have been elaborated up to now, although
several simple patterns can be confidently reproduced by the code
with drying/wetting technique over fixed grid.

Numerical solution of IBV problem for flow equations is obtained
in Finite Volume convention by approximate Riemann solvers technique,
which enables automatic capturing of discontinuities as well as
high-resolution numerical solutions fulfilling the energy inequality.
Spatial resolution is achieved by componentwise MUSCL formulation with
limiting gradients of conserved fields.

A variety of time-marching integrators is provided, including explicit
2-nd order Adams and Runge-Kutta rules, weighted implicit Crank-Nicholson
and midpoint rules. Alternate-direction implicit rules (ADI) are under
construction.