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This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical parameters or stabilization parameters. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed method.
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Parameter-robust multiphysics algorithms for Biot model with application in brain edema simulation
In this paper, we develop parameter-robust numerical algorithms for Biot model and apply the algorithms in brain edema simulations. By introducing an intermediate variable, we derive a multiphysics reformulation of the Biot model. Based on the reformulation, the Biot model is viewed as a generalized Stokes subproblem combining with a reaction–diffusion subproblem. Solving the two subproblems together or separately leads to a coupled or a decoupled algorithm. We conduct extensive numerical experiments to show that the two algorithms are robust with respect to the key physical parameters. The algorithms are applied to study the brain swelling caused by abnormal accumulation of cerebrospinal fluid in injured areas. The effects of the key physical parameters on brain swelling are carefully investigated. It is observed that the permeability has the biggest influence on intracranial pressure (ICP) and tissue deformation; the Young’s modulus and the Poisson ratio do not affect the maximum value of ICP too much but have big influence on the tissue deformation and the developing speed of brain swelling.
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- PAR ID:
- 10178652
- Date Published:
- Journal Name:
- Mathematics and computers in simulation
- Volume:
- 177
- ISSN:
- 0378-4754
- Page Range / eLocation ID:
- 385-403
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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This paper is concerned with numerical algorithms for Biot model. By introducing an intermediate variable, the classical 2-field Biot model is written into a 3-field formulation. Based on such a 3-field formulation, we propose a coupled algorithm, some time-extrapolation based decoupled algorithms, and an iterative decoupled algorithm. Our focus is the analysis of the iterative decoupled algorithm. It is shown that the convergence of the iterative decoupled algorithm requires no extra assumptions on physical parameters or stabilization parameters. Numerical experiments are provided to demonstrate the accuracy and efficiency of the proposed method.more » « less
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We study numerical algorithms for solving Biot’s model. Based on a three-field reformulation, we present some algorithms that are inspired by the work of Chaabane et al. (Comput MathAppl 75(7):2328–2337) and Lee (Unconditionally stable second order convergent partitioned methods for multiple-network poroelasticity arXiv:1901.06078, 2019) for decoupling the computation of Biot’s model. A new theoretical framework is developed to analyze the algorithms. Considering a uniform temporal discretization, these algorithms solve the coupled model on the first time level. On the remaining time levels, one algorithm solves a reaction-diffusion subproblem first and then solves a generalized Stokes subproblem.Another algorithm reverses the order of solving the two subproblems. Our algorithms manage to decouple the numerical computation of the coupled system while retaining the convergence properties of the original coupled algorithm. Theoretical analysis is conducted to show that these algorithms are unconditionally stable and optimally convergent.Numerical experiments are also carried out to validate the theoretical analysis and demonstrate the advantages of the proposed algorithms.more » « less
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Abstract We present a new computational fluid dynamics approach for simulating two‐phase flow in hybrid systems containing solid‐free regions and deformable porous matrices. Our approach is based on the derivation of a unique set of volume‐averaged partial differential equations that asymptotically approach the Navier‐Stokes Volume‐of‐Fluid equations in solid‐free regions and multiphase Biot Theory in porous regions. The resulting equations extend our recently developed Darcy‐Brinkman‐Biot framework to multiphase flow. Through careful consideration of interfacial dynamics (relative permeability and capillary effects) and extensive benchmarking, we show that the resulting model accurately captures the strong two‐way coupling that is often exhibited between multiple fluids and deformable porous media. Thus, it can be used to represent flow‐induced material deformation (swelling, compression) and failure (cracking, fracturing). The model's open‐source numerical implementation,hybridBiotInterFoam, effectively marks the extension of computational fluid mechanics into modeling multiscale multiphase flow in deformable porous systems. The versatility of the solver is illustrated through applications related to material failure in poroelastic coastal barriers and surface deformation due to fluid injection in poro‐visco‐plastic systems.more » « less
- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1016/j.matcom.2020.04.027
