2022/06/29 by Nicholas J. Derr, Chris H. Rycroft, Derr, Nicholas J. +1
Computer Science · Mathematics · Physics and Astronomy · #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Numerical Analysis (math.NA) #Soft Condensed Matter (cond-mat.soft) #cond-mat.soft #cs.NA #math.NA #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.2206.14379
16 pages, 3 figures
arxiv created 2022/06/29 · arxiv updated 2022/06/30
Flow through porous, elastically deforming media is present in a variety of natural contexts ranging from large-scale geophysics to cellular biology. In the case of incompressible constituents, the porefluid pressure acts as a Lagrange multiplier to satisfy the resulting constraint on fluid divergence. The resulting system of equations is a possibly non-linear saddle-point problem and difficult to solve numerically, requiring nonlinear implicit solvers or flux-splitting methods. Here, we present a method for the simulation of flow through porous media and its coupled elastic deformation. The pore pressure field is calculated at each time step by correcting trial velocities in a manner similar to Chorin projection methods. We demonstrate the method's second-order convergence in space and time and show its application to phase separating neo-Hookean gels.