Non-conforming FEM/BEM Coupling for Wave Propagation in Poroelastic Media

Research Area

In many engineering applications wave propagation phenomena in coupled domains have to be studied, e.g., a dam-reservoir system. Unbounded domains with a linear description of the domain are effectively treated by the Boundary Element Method (BEM), whereas non-linear bounded domains are treated well by the Finite Element Method (FEM). That is why often a coupled approach of both methodologies is used.
With Mortar methods different mesh sizes and different physical domains, e.g., a poroelastic domain and a fluid domain, can be coupled effectively.

State of the Art

Both, poroelastic FE and BE formulations exist to solve wave propagation problems numerically. Based on Biot's theory of poroelasticity [1,2] a time dependent BE formulation was published by Schanz [4]. Also poroelastodynamic FE formulations are given, e.g., by Zienkiewicz et al. [5].
Unfortunately, for poroelastic continua not too much publication on a FE/BE coupling are available, especially with non-conforming interfaces. FE/BE coupling which enables different meshes can be achieved with Mortar Methods as published for elastodynamics in [3].

Project Topics

The aim of this project is to formulate, analyse, implement, and provide an efficient simulation tool based on a coupled finite and boundary element method for poroelastodynamics.
The key points of this project are

• to develop a well modularized software, using existing libraries (FEM, BEM),
• to establish a Mortar formulation for FE/BE coupling,
• to formulate coupling conditions for multi-physic problems, e.g., for a coupling of a fluid and poroelastic domain.

References

[1]

M.A. Biot. Theory of propagation of elastic waves in fluid-saturated porous solid. I. Lower frequency range. J. Acoust. Soc. Am., 28(2):168-178, 1956.

[2]

M.A. Biot. Theory of propagation of elastic waves in fluid-saturated porous solid. I. Lower frequency range. J. Acoust. Soc. Am., 28(2):179-191, 1956.

[3]

T. Rüberg. Non-conforming FEM/BEM Coupling in Time Domain, volume 3 of Computation in Engineering and Science. Verlag der Technischen Universität Graz, 2007.

[4]

M. Schanz. Wave Propagation in Viscoelastic and Poroelastic Continua: A Boundary Element Approach, volume 2 of Lecture Notes in Applied Mechanics. Springer-Verlag, Berlin, Heidelberg, New York, 2001.

[5]

O.C. Zienkiewicz and T. Shiomi. Dynamic behavior of saturated porous media: The generalized Biot formulation and its numerical solution. Int. J. Numer. Anal. Methods Geomech., 8(1):71-96, 1984.