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Description of the depth-averaged two-phase flow code in hpGEM

Summary: Description of the depth-averaged
two-phase flow code in hpGEM
Sander Rhebergen
1 Introduction
In this note we give a description of the implementation of the discontinuous Galerkin fi-
nite element discretization of the depth-averaged two-phase 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 x1-x2 plane with the horizontal. Depth-averaged 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


Source: Al Hanbali, Ahmad - Department of Applied Mathematics, Universiteit Twente


Collections: Engineering