Spatial stability for the monolithic and sequential methods with various space discretizations in poroelasticity. (8th February 2018)

• Record Type: Journal Article
• Authors: Yoon, Hyun C.; Kim, Jihoon
• Is Part Of: International journal for numerical methods in engineering. Volume 114:Number 7(2018)
• Page Start: 694
• Page End: 718
• Publication Date: 2018-02-08
• Subjects: discontinuity -- fixed‐stress split -- inf‐sup condition -- spurious oscillation -- stabilization; Numerical analysis -- Periodicals; Engineering mathematics -- Periodicals; 620.001518
• DOI: 10.1002/nme.5762
• Languages: English
• ISSNs: 0029-5981

Abstract

Summary: We investigate spatial stability with various numerical discretizations in displacement and pressure fields for poroelasticity. We study 2 sources of the early time instability: discontinuity of pressure and violation of the inf‐sup condition. We consider both compressible and incompressible fluids by employing the monolithic, stabilized monolithic, and fixed‐stress sequential methods. Four different spatial discretization schemes are used: Q1Q1, Q2Q1, Q1P0, and Q2P0. From mathematic analysis and numerical tests, the piecewise constant finite volume method for flow provides stability at the early time for the case of the pressure discontinuity. On the other hand, a piecewise continuous (or higher‐order) interpolation of pressure shows spatial oscillation, having lower limits of time step size, although lower approximations of pressure than displacement can alleviate the oscillation. For an incompressible fluid, Q2Q1 can be better than Q1P0, because Q1P0 might not satisfy the inf‐sup condition. However, regardless of fluid compressibility and the pressure discontinuity, the fixed‐stress method can effectively stabilize the oscillation without an artificial stabilizer. Even when Q1P0 and Q1Q1 with the monolithic method cannot satisfy the inf‐sup condition, the fixed‐stress method can yield the full‐rank linear system, providing stability. Thus, the fixed‐stress method with Q1P0 can effectively circumvent the aforementioned 2 types of instability.