Efficient pseudo-spectral solvers for the PKN model of hydrofracturing
Provides an efficient numerical method for simulating hydraulic fracturing, relevant to geophysics and engineering applications.
The paper develops a pseudo-spectral algorithm for the PKN hydrofracturing model that computes both solution and temporal derivative, achieving excellent cost-effectiveness in accuracy versus mesh density trade-offs across various leak-off regimes.
In the paper, a novel algorithm employing pseudo-spectral approach is developed for the PKN model of hydrofracturing. The respective solvers based on this approach compute both the solution and its temporal derivative. In comparison with conventional solvers, they demonstrate excellent cost effectiveness in terms of balance between the accuracy of computations and densities of the temporal and spatial meshes. Various leak-off regimes are considered.