80 citations · 367 across the 24 of their papers we have counts for
10 papers · 1 filter
On the optimization of the fixed-stress splitting for Biot's equations
Erlend Storvik, Jakub Wiktor Both, Kundan Kumar +2
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider the fixed-stress splitting scheme, which is a popular metho…
A Singularity Removal Method for Coupled 1D-3D Flow Models
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten
In reservoir simulations, the radius of a well is inevitably going to be small compared to the horizontal length scale of the reservoir. For this reason, wells are typically modell…
Splitting method for elliptic equations with line sources
Ingeborg G. Gjerde, Kundan Kumar, Jan M. Nordbotten +1
In this paper, we study the mathematical structure and numerical approximation of elliptic problems posed in a (3D) domain when the right-hand side is a (1D) line source . T…
An upscaled model for permeable biofilm in a thin channel and tube
David Landa-Marbán, Gunhild Bødtker, Kundan Kumar +2
In this paper, we derive upscaled equations for modelling biofilm growth in porous media. The resulting macro-scale mathematical models consider permeable multi-species biofilm inc…
A pore-scale model for permeable biofilm: numerical simulations and laboratory experiments
David Landa-Marbán, Na Liu, Iuliu Sorin Pop +5
In this paper we derive a pore-scale model for permeable biofilm formation in a two-dimensional pore. The pore is divided in two phases: water and biofilm. The biofilm is assumed t…
Guaranteed and computable error bounds for approximations constructed by an iterative decoupling of the Biot problem
Kundan Kumar, Svetlana Kyas, Jan Nordbotten +1
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 equat…