Influences on mass conservation within growth of porous materials utilising nondimensionalisation
Please login to view abstract download link
Growth occurs within different engineering applications, such as freezing in saturated soil and pancake ice or tissue growth within biomaterials. Depending on parameters such as the density ratio, permeability or compressibility of the solid matrix, either small or finite deformations occur. In the small deformation regime, simplified models with restricted validity can be derived. Resulting solution strategies show better stability properties and a reduced computational complexity, compared to the fully non-linear approaches. Within this talk, growth processes in porous media are discussed. In order to clarify the interaction of the different model parameters, a non-dimensional from of the Theory of Porous Media (TPM) is presented, based on which effects of simplified models on accuracy and mass conservation are highlighted. Beside these influences from the model itself, the accuracy of the approximated solution play a vital role within application. Especially, the accuracy of the flux is crucial. We will therefore address influences of mixed discretisations for the flow-field [1] or adaptive solution strategies based on flux reconstruction [2]. REFERENCES [1] Mardal KA., Rognes M.E. and Thompson T.B. Accurate discretization of poroelasticity without Darcy stability. BIT Numer. Math. (2021) 61: 941–976 [2] Bertrand F. and Starke G. A posteriori error estimates by weakly symmetric stress reconstruction for the Biot problem. Comput. Math. with Appl. (2021) 91: 3-16
