The paper describes the application of front tracking to the polymer system
, an example of a nonstrictly hyperbolic system. Front tracking computes pi
ecewise constant approximations based on approximate Riemann solutions and
exact tracking of waves. It is well known that the front tracking method ma
y 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, and that this time decreases with the
discretization parameter.
For multidimensional problems, front tracking is combined with dimensional
splitting, and numerical experiments indicate that large splitting steps ca
n be used without loss of accuracy. Typical CFL numbers are in the range 10
-20, and comparisons with Riemann free, high-resolution methods confirm 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 a
re presented, where this model is solved by a sequential time stepping proc
edure. Because of the approximate Riemann solver, the method is non-conserv
ative and CFL numbers must be chosen only moderately larger than unity to a
void substantial material balance errors generated in near-well regions aft
er water breakthrough. Moreover, it is demonstrated that dimensional splitt
ing may introduce severe grid orientation effects for unstable displacement
s that are accentuated for decreasing discretization parameters.