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Numerical discretizations of the Generalized Porous Medium Equation (GPME)with discontinuous coefficients are analyzed with respect to the formation ofnumerical artifacts. In addition to the degeneracy and self-sharpening of theGPME with continuous coefficients, detailed in [1], increased numericalchallenges occur in the discontinuous coefficients case. These numericalchallenges manifest themselves in spurious temporal oscillations in secondorder finite volume discretizations with both arithmetic and harmonicaveraging. The integral average, developed in [2] leads to improved solutionswith monotone and reduced amplitude temporal oscillations. In this paper, wepropose a new method called the Shock-Based Averaging Method (SAM) thatincorporates the shock position into the numerical scheme. The shock positionis numerically calculated by discretizing the theoretical speed of the frontfrom the GPME theory. The speed satisfies the jump condition for integralconservation laws. SAM results in a non-oscillatory temporal profile, producingphysically valid numerical results. We use SAM to demonstrate that the choiceof averaging alone is not the cause of the oscillations, and that the shockposition must be a part of the numerical scheme to avoid the artifacts.

Numerical Artifacts in the Discontinuous Generalized Porous Medium Equation: How to Avoid Spurious Temporal Oscillations