Efficient pseudo-spectral solvers for the PKN model of hydrofracturing

TL;DR

This paper introduces a novel pseudo-spectral algorithm for the PKN hydrofracturing model, offering efficient and accurate solutions with improved computational cost over traditional methods across different leak-off regimes.

Contribution

The paper presents a new pseudo-spectral solver for the PKN model that enhances computational efficiency and accuracy compared to conventional approaches.

Findings

Demonstrates superior cost-effectiveness of the proposed solver

Achieves high accuracy with fewer mesh points

Effective across various leak-off regimes

Abstract

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.