SCAIM Seminar: A hybrid asymptotic-Hermite Cubic scheme for solving Plane Strain Hydraulic Fracture Problems
Speakers
Details
In this talk I will describe
the coupled integro-partial differential equations that model the
evolution of a fluid-driven fracture propagating in a state of plain
strain. I will discuss the use of the Mellin Transform and matched
asymptotics to establish the asymptotic behavior of the solution in the
vicinity of the fracture tip for a number of regimes of propagation. I
also describe a novel cubic Hermite collocation scheme to solve these
coupled equations. This algorithm involves special blended cubic
Hermite-power law basis functions, with an arbitrary index 0<1,
which are developed to treat the singular behavior of the solution that
typically occurs at the tips of a hydraulic fracture. I also discuss
the implementation of blended infinite elements to model semi-infinite
crack problems. The cubic Hermite collocation algorithm is used to
solve a number of different test problems and the results are compared
to published similarity, asymptotic, and numerical solutions.
