Berger Lorenz, Bordas Rafel, Kay David, Tavener Simon
Innersight Labs, 7 Astbury House, Lambeth Walk, London, SE11 6LZ UK.
Roxar Ltd, Emerson Process Management, Northbrook House, Oxford Science Park, Oxford, OX4 4GA UK.
Comput Mech. 2017;60(1):51-68. doi: 10.1007/s00466-017-1381-8. Epub 2017 Mar 1.
We construct a stabilized finite-element method to compute flow and finite-strain deformations in an incompressible poroelastic medium. We employ a three-field mixed formulation to calculate displacement, fluid flux and pressure directly and introduce a Lagrange multiplier to enforce flux boundary conditions. We use a low order approximation, namely, continuous piecewise-linear approximation for the displacements and fluid flux, and piecewise-constant approximation for the pressure. This results in a simple matrix structure with low bandwidth. The method is stable in both the limiting cases of small and large permeability. Moreover, the discontinuous pressure space enables efficient approximation of steep gradients such as those occurring due to rapidly changing material coefficients or boundary conditions, both of which are commonly seen in physical and biological applications.
我们构造了一种稳定有限元方法，用于计算不可压缩多孔弹性介质中的流动和有限应变变形。我们采用三场混合公式直接计算位移、流体通量和压力，并引入拉格朗日乘子来施加通量边界条件。我们使用低阶近似，即位移和流体通量采用连续分段线性近似，压力采用分段常数近似。这导致了一个具有低带宽的简单矩阵结构。该方法在渗透率小和大的极限情况下都是稳定的。此外，不连续压力空间能够有效地近似陡峭梯度，例如由于材料系数或边界条件快速变化而出现的梯度，这两种情况在物理和生物应用中都很常见。
