Conference Agenda

A riverbed is a porous medium consisting of a granular skeleton and the pore fluid, which itself comprises water and air. In quasi-saturated conditions, the degree of water saturation ranges from 85 - 99 %. Hydrodynamic boundary conditions affected by, e.g., ship passage influence the hydro-mechanical state of the riverbed. When the intergranular contact forces disappear due to an increase in (excess) pore water pressure, liquefaction occurs, at this point the soil behaves like a fluid instead of a solid. This can lead for example to sediment movement, destabilization of bank protection measures, washed-out submarine pipelines or damaged coastal structures. Modeling of this process requires strong hydro-mechanical coupling and the possibility to represent large deformations. The FEniCS framework was used to solve the underlying partial differential equations in a Lagrangian setting using the finite element method. In addition to the process description, the underlying material model for the soil particle phase must be able to correctly represent the transition from a solid-like to a fluid-like behavior. To date, no approach available in geotechnical software is able to satisfactorily represent the entire process for all associated phases. First steps towards this direction will be shown coupling FEniCS with MFront, which offers the possibility to implement different material models and to incorporate them into different programs via a generic interface. Through this procedure the use of different software packages and even numerical methods becomes practically feasible. First steps towards the identification of a material model, which can represent the bidirectional phase change during liquefaction, will be shown. Experimental data sets generated in a soil column in combination with an alternating flow apparatus serve as a basis for comparison.

Flow in porous media can be described by the Darcy model in a wide range of applications from soil mechanics to biomechanics. Many relevant applications manifest large scale problems that require transient simulations and finely resolved discretizations. With currently available algorithmic approaches, this can lead to impractically high computing costs or demand to exclude certain effects. For example, current poroelastic models of the human lungs generally solve the steady-state Darcy equation, leaving transient effects unstudied. To address this matter, we propose a new solver for the unsteady Darcy flow problem in anisotropic porous media with spatially and temporally variable porosity and permeability fields.

We use the discontinuous Galerkin method with L2-conforming tensor-product elements for the spatial discretization, and the BDF method for the temporal discretization of the Darcy flow equations. We solve the resulting coupled pressure-velocity system by matrix-free implementation techniques for operator evaluation in Krylov solvers as well as preconditioners. To ensure fast convergence of the solvers, we identify spectrally equivalent preconditioners based on the so-called block preconditioning technique with approximate inverses of the velocity-velocity block and of the Schur complement of the coupled system. For the velocity-velocity block, we design a matrix-free cellwise inverse mass operator with variable coefficients. To minimize arithmetic work, we exploit the tensor-product structure of shape functions using a technique known as sum-factorization. On the other hand, a hybrid multigrid preconditioner for the Poisson problem with variable coefficients approximates the inverse of the Schur complement. We expect these methods to lay a new foundation for high-performance numerical simulations of general Darcy flow.

All methods and applications are implemented in the open source software projects ExaDG and deal.II.

We use numerical simulations to investigate the mixing dynamics of a convection-driven porous media flow. We consider a fully saturated homogenous and isotropic porous medium, in which the flow is driven by density differences induced by the presence of a solute. In particular, the fluid density is a linear function of the solute concentration. The configuration considered is representative of geological applications in which a solute is transported and dissolves as a result of a density-driven flow, such as in carbon sequestration in saline formations or water contamination processes. The mixing mechanism is made complex by the presence of rocks (solid objects), which represent obstacles in the flow and make the solute to further spread, due to the continue change of the fluid path. Making accurate predictions on the dynamics of this time-dependent system is crucial to provide reliable estimates of the evolution of subsurface flows, and in determining the controlling parameters, e.g., the injection rate of a current of carbon dioxide or the spreading of a pollutant in underground formations. To model this process, we consider here an unstable and time-dependent configuration defined as Rayleigh-Taylor instability, where a heavy fluid (saturated with solute) initially sits on top of a lighter one (without solute). The fluids are fully miscible, and the mixing process is characterised by the interplay of diffusion and advection: initially diffusion controls the flow and is responsible for the initial mixing of solute. At a later stage, the action of gravity promotes the formation of instabilities, and efficient fluid mixing takes place over the entire domain. The competition between buoyancy and diffusion is measured by the Rayleigh-Darcy number (Ra), the value of which controls the entire dynamics of the flow. We analyse the time-dependent evolution of this system at high Ra, and we quantify the effect of the Rayleigh-Darcy number on solute transport and mixing. Simulations are performed with a highly parallelized finite difference (FD) code coupled with immersed boundaries method (IBM) to account for the presence of the solid obstacles. We compare the results against experimental measurements in bead packs. The results are analysed at two different flow scales: i) at the Darcy, where the buoyancy-driven plumes control the flow dynamics, and ii) at the pore-scale, where diffusion promotes inter-pore solute mixing. Numerical and experimental measurements are used to design simple physical models to describe the mixing state and the mixing length of the system.