 
Summary: Description of the depthaveraged
twophase flow code in hpGEM
Sander Rhebergen
23062009
1 Introduction
In this note we give a description of the implementation of the discontinuous Galerkin fi
nite element discretization of the depthaveraged twophase flow equations as formulated in
Rhebergen et al. [9]. The equations are of hyperbolic type (depending, however, on the pa
rameters required  if parameters are chosen such that the equations are not hyperbolic, this
code does not work). Furthermore, the PDE's have nonconservative products and we deal
with these terms as described in [8] based on the theory of Dal Maso, LeFloch and Murat [1].
To deal with over and undershoots, a WENO slope limiter is applied [6, 9] in conjunction
with a discontinuity detector [4, 9].
2 The equations
Let the orientation of the Cartisian coordinate system be as is shown in Figure 1 in which
is the angle of the x1x2 plane with the horizontal. Depthaveraged variables are the par
ticle volume fraction , the fluid velocity vector u = (u1, u2) and the solids velocity vector
v = (v1, v2) which are constant in the x3 direction. The flow depth is given by h and the
bottom topography by b. The constants = H/L and = f /s represent the height to
length ratio of the flow and the ratio between the fluid density f and the solids density
