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

  • Schanz, Martin (Principal Investigator (PI))
  • Rammerstorfer, Franz, (Co-Investigator (CoI))

Project: Research project

Description

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.
StatusFinished
Effective start/end date1/08/0831/08/14