Analytic solutions and transmission eigenvalues in isotropic poroelasticity for bounded domain, scattering of obstacles and fluid-solid interaction problems in 2D

Overview & Synopsis

In this report, we construct analytical solutions and study numerically the well-posedness of several problems concerning the isotropic poroelastic equation in axisymmetry. Theproblems in consideration are cylindrical bounded domains, the scattering of plane wave in poroe-lastic by penetrable/impenetrable circular obstacles and lastly fluid-solid interaction problem withcircular solid obstacles for closed, open and intermediate pore boundary type. Since we have an-alytic expressions for the coefficients / transmission matrices, well-posedness is investigated byprobing for zeros of the determinant of these matrices. Our investigation includes the effect ofmaterial parameters and different degrees of viscosity. The first novelty of the work is the proposalof a definition of outgoing solutions for isotropic poroelasticity. The second novelty is the obser-vation that there are modes in fluid-poroelastic interaction problems without viscosity which arethe equivalent of Jones’ modes for fluid-elastic problem, and that these modes cease to exist in thepresence of viscosity. We found out that the presence of viscosity removes the eigenvalues, whichexist without viscosity and whose existence is expected for bounded domains.