Instability in Runge-Kutta schemes for simulation of oil recovery (Q759470)

Runge-Kutta schemes have been of interest to increase the maximum stable timestep for implicit pressure, explicit saturation (IMPES) numerical schemes for oil recovery. This stabilized method is based on the work of \textit{P. J. van der Houwen} [Construction of integration formulas for initial value problems (1977; Zbl 0359.65057)] for parabolic problems. This work demonstrates that the maximum timesteps of van der Houwen do not apply to this hyperbolic system. Indeed, for some problems the stabilized method is less efficient than the ordinary IMPES method. Some test calculations verify the result.