Svetlana Kyas | Searcharxiv

arXiv2020

Accelerated reactive transport simulations in heterogeneous porous media using Reaktoro and Firedrake

This work investigates the performance of the on-demand machine learning (ODML) algorithm introduced in Leal et al. (2020) when applied to different reactive transport problems in heterogeneous porous media. ODML was devised to accelerate the computationally expensive geochemical reaction calculations in reactive transport simulations. We demonstrate that the ODML algorithm speeds up these calculations by one to three orders of magnitude. Such acceleration, in turn, significantly accelerates the entire reactive transport simulation. The numerical experiments are performed by implementing the coupling of two open-source software packages: Reaktoro (Leal, 2015) and Firedrake (Rathgeber et al., 2016).

cs.CE↗

arXiv2020

Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem

The paper is concerned with guaranteed a posteriori error estimates for a class of evolutionary problems related to poroelastic media governed by the quasi-static linear Biot equations. The system is decoupled employing the fixed-stress split scheme, which leads to a semi-discrete system solved iteratively. The error bounds are derived by combining a posteriori estimates for contractive mappings with those of the functional type for elliptic partial differential equations. The estimates are applicable for any approximation in the admissible functional space and are independent of the discretization method. They are fully computable, do not contain mesh dependent constants, and provide reliable global estimates of the error measured in the energy norm. Moreover, they suggest efficient error indicators for the distribution of local errors, which can be used in adaptive procedures.

math.NA↗