A5101505057- Advanced Numerical Methods in Computational Mathematics
- Advanced Mathematical Modeling in Engineering
- Groundwater flow and contamination studies
- Numerical methods in engineering
- Computational Fluid Dynamics and Aerodynamics
- Soil and Unsaturated Flow
- CO2 Sequestration and Geologic Interactions
- Enhanced Oil Recovery Techniques
- Composite Material Mechanics
- Numerical methods for differential equations
- Hydraulic Fracturing and Reservoir Analysis
- Differential Equations and Numerical Methods
- Electromagnetic Simulation and Numerical Methods
- Elasticity and Material Modeling
- Heat and Mass Transfer in Porous Media
- Dam Engineering and Safety
- Lattice Boltzmann Simulation Studies
- Hydrocarbon exploration and reservoir analysis
- Fluid Dynamics and Turbulent Flows
- Fluid Dynamics and Thin Films
- Matrix Theory and Algorithms
- Solidification and crystal growth phenomena
- Numerical methods in inverse problems
- Electromagnetic Scattering and Analysis
- Particle Dynamics in Fluid Flows
University of Bergen
2015-2024
Hasselt University
2020
Princeton University
2017
Helmholtz Centre for Environmental Research
2007-2014
Friedrich Schiller University Jena
2007-2011
Friedrich-Alexander-Universität Erlangen-Nürnberg
2002-2011
Max Planck Institute for Mathematics in the Sciences
2007-2008
Max Planck Institute for Mathematics
2008
Max Planck Society
2008
This work concerns linearization methods for efficiently solving the Richards` equation,a degenerate elliptic-parabolic equation which models flow in saturated/unsaturated porous media.The discretization of is based on backward Euler time and Galerkin finite el-ements space. The most valuable schemes equation, i.e. Newtonmethod, Picard method, Picard/Newton method theLscheme are presented theirperformance comparatively studied. convergence, computational conditionnumbers underlying linear...
In this work we consider a mathematical model for two-phase flow in porous media. The fluids are assumed immiscible and incompressible the solid matrix non-deformable. is written terms of global pressure complementary (obtained by using Kirchhoff transformation) as primary unknowns. For spatial discretization, finite volumes have been used (more precisely multi-point flux approximation method) time backward Euler method has employed. We present here new linearization scheme nonlinear system...
In this paper, we study the robust linearization of nonlinear poromechanics unsaturated materials. The model interest couples Richards equation with linear elasticity equations, employing equivalent pore pressure. practice a monolithic solver is not always available, defining requirement for scheme to allow use separate simulators, which met by classical Newton method. We propose three different schemes incorporating fixed-stress splitting scheme, coupled an L-scheme, Modified Picard and...
In this work we are interested in effectively solving the quasi-static, linear Biot model for poromechanics. We consider fixed-stress splitting scheme, which is a popular method iteratively Biot's equations. It well-known that convergence of strongly dependent on applied stabilization/tuning parameter. work, propose new approach to optimize show theoretically it depends also fluid flow properties and not only mechanics coupling coefficient. The type analysis presented paper restricted...
We consider a numerical scheme for class of degenerate parabolic equations, including both slow and fast diffusion cases. A particular example in this sense is the Richards equation modeling flow porous media. The based on mixed finite element method (MFEM) space, one step implicit time. lowest order Raviart–Thomas elements are used. Here we extend results Radu et al. (SIAM J Numer Anal 42:1452–1478, 2004), Schneid (Numer Math 98:353–370, 2004) to more general framework, by allowing types...
Abstract Spatial discretization of transport and transformation processes in porous media requires techniques that handle general geometry, discontinuous coefficients are locally mass conservative. Multi‐point flux approximation (MPFA) methods such techniques, we will here discuss some formulations on triangular grids with further application to the nonlinear Richards equation. The MPFA be rewritten mixed form derive stability conditions error estimates. Several versions shown, discussed...
This paper concerns the analysis and implementation of a novel iterative staggered scheme for quasi-static brittle fracture propagation models, where evolution is tracked by phase field variable. The model we consider two-field variational inequality system, with function elastic displacements solid material as independent variables. Using penalization strategy, this system transformed into equality which formulation take starting point our algorithmic developments. proposed involves...
There is currently an increasing interest in developing efficient solvers for phase-field modeling of brittle fracture. The governing equations this problem originate from a constrained minimization non-convex energy functional, and the most commonly used solver staggered solution scheme. This known to be robust compared monolithic Newton method, however, scheme often requires many iterations converge when cracks are evolving. focus our work accelerate through that sequentially applies...
We analyze a discretization method for class of degenerate parabolic problems that includes the Richards' equation. This analysis applies to pressure-based formulation and considers both variably fully saturated regimes. To overcome difficulties posed by lack in regularity, we first apply Kirchhoff transformation then integrate resulting equation time. state conformal mixed variational prove their equivalence. will be underlying idea our technique get error estimates. A regularization...
In this article, we analyze an Euler implicit-mixed finite element scheme for a porous media solute transport model. The transporting flux is not assumed given, but obtained by solving numerically the Richards equation, model subsurface fluid flow. We prove convergence of estimating error in terms discretization parameters. doing so take into account numerical occurring approximation concluded experiments, which are good agreement with theoretical estimates. © 2009 Wiley Periodicals, Inc....
Abstract Motivated by rock–fluid interactions occurring in a geothermal reservoir, we present two-dimensional pore scale model of periodic porous medium consisting void space and grains, with fluid flow through the space. The ions are allowed to precipitate onto while minerals grains dissolve into fluid, take account possible change geometry that these two processes cause, resulting problem free boundary at scale. We include temperature dependence effects both properties mineral...
In this work, we present a mass conservative numerical scheme for two-phase flow in porous media. The model consists of two fully coupled, nonlinear equations: degenerate parabolic equation and an elliptic one. proposed is based on backward Euler the temporal discretization mixed finite element method spatial A priori stability error estimates are presented to prove convergence scheme. monotone increasing, Hölder continuous saturation considered. naturally dependant exponent. systems within...
Abstract Biodegradable collagen matrices have become a promising alternative to traditional drug delivery systems. The relevant mechanisms in controlled release are the diffusion of water into matrix, swelling matrix coming along with release, and enzymatic degradation additional simultaneous release. These phenomena been extensively studied past experimentally, via numerical simulations as well analytically. However, rigorous derivation macroscopic model description, which includes evolving...
In this paper we develop adaptive iterative coupling schemes for the Biot system modeling coupled poromechanics problems. We particularly consider space–time formulation of fixed-stress scheme, in which first solve problem flow over whole interval, then exploiting information solving mechanics. Two common discretizations algorithm are introduced based on two mixed finite element methods in-space and backward Euler scheme in-time. Therefrom, algorithms build conforming reconstructions...