Sammendrag
The paper describes the application of front tracking to the polymer system,
an example of a nonstrictly hyperbolic system. Front tracking computes
piecewise constant approximations based on approximate Riemann solutions and
exact tracking of waves.
It is well--known that the front tracking method may introduce a
blowup of the initial total variation for initial data along the
curve where the two eigenvalues of the hyperbolic system are
identical. It is demonstrated by numerical examples that the method
converges to the correct solution after a finite time that decreases
with the discretization parameter.
For multidimensional problems, front tracking is combined with dimensional
splitting and numerical experiments indicate that large splitting steps can
be used without loss of accuracy. Typical CFL numbers are in the range 10
to 20, and comparisons with Riemann free, high--resolution methods
confirm that the high efficiency of front tracking.
The polymer system, coupled with an elliptic pressure equation, models
two-phase, three-component polymer flooding in an oil reservoir. Two
examples are presented, where this model is solved by a sequential time
stepping procedure. Because of the approximate Riemann solver, the method is
non-conservative and \CFL\ numbers must be chosen only moderately larger
than unity to avoid substantial material balance errors generated in
near-well regions after water breakthrough. Moreover, it is demonstrated
that dimensional splitting may introduce severe grid orientation effects for
unstable displacements that are accentuated for decreasing discretization
parameters.
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