An Immersed Interface Method for a 1D Poroelasticity Problem with Discontinuous Coefficients

Poroelastic models deal with the coupling of changes in stress and fluid pressure in some porous medium. For physical reasons, some of the coefficients used in the models may have discontinuities. This project focuses on applying the immersed interface method to the one dimensional Biot model, in order to handle these discontinuities. This method is applied on a staggered grid. Using the immersed interface method allows us to alter only a small number of irregular grid points surrounding a discontinuity. For most of the grid points, a standard finite difference method is used. However at the irregular grid points, the method of undetermined coefficients is used to improve the standard approximation. Finally numerical experiments are carried out to confirm an expected convergence rate of O(h + dt)