On a decoupled solver for Biot’s equations using isogeometric analysis
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In this work, we propose an iterative solver to eliminate non-physical oscillations in the pressure approximation of Biot's model for poroelasticity under low permeabilities and/or small time steps. Our approach first solves the flow problem, followed by the mechanics, in a manner similar to the so-called fixed-stress splitting method. The suppression of spurious oscillations is achieved through a novel stabilization that also ensures the convergence of the iterative solver. In addition, we introduce a new parameter to optimize the convergence of the numerical scheme. For discretization, we apply the isogeometric extension of Taylor-Hood elements. Finally, we will show some numerical results to demonstrate the efficiency and robustness of our solver with respect to both discretization and physical parameters.