A5073728063- Advanced Mathematical Modeling in Engineering
- Advanced Numerical Methods in Computational Mathematics
- Groundwater flow and contamination studies
- Physics and Engineering Research Articles
- Computational Fluid Dynamics and Aerodynamics
- Differential Equations and Numerical Methods
- Soil and Unsaturated Flow
- Numerical methods in inverse problems
- Engineering and Materials Science Studies
- Lattice Boltzmann Simulation Studies
- Numerical methods for differential equations
- Enhanced Oil Recovery Techniques
- CO2 Sequestration and Geologic Interactions
- Composite Material Mechanics
- Advanced Numerical Analysis Techniques
- Nonlinear Partial Differential Equations
- Numerical methods in engineering
- History and Theory of Mathematics
- Mathematics and Applications
- Hydraulic Fracturing and Reservoir Analysis
- Electromagnetic Simulation and Numerical Methods
- Toxic Organic Pollutants Impact
- Solidification and crystal growth phenomena
- Civil and Structural Engineering Research
- Advanced Theoretical and Applied Studies in Material Sciences and Geometry
Friedrich-Alexander-Universität Erlangen-Nürnberg
2015-2024
University of Stuttgart
2023
Simulation Technologies (United States)
2023
Forschungszentrum Jülich
2011
Applied Mathematics (United States)
2002-2006
Eindhoven University of Technology
2004
University of Augsburg
1983-2003
Institute of Applied Mathematics
1999
Weierstrass Institute for Applied Analysis and Stochastics
1993
Augsburg University
1985-1986
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...
In this paper, we are dealing with the mathematical modeling and homogenization of nonlinear reaction-diffusion processes in a porous medium that consists two components separated by an interface. One is connected, other one disconnected periodically distributed inclusions. At interface, fluxes given functions concentrations on both sides Thus, may be discontinuous across For derivation effective (homogenized) model, use method two-scale convergence. To prove convergence terms, especially...
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 a systematic approach for the efficient computation of transport and reaction multispecies, multireaction system is proposed. The objective to reformulate given differential or differential‐algebraic equations in such way that couplings nonlinearities are concentrated reduced number (if compared original formulation), while some linear decouple from system. resulting handled spirit global implicit (“one step method”) avoiding operator splitting techniques. reduction problem...
A new systematic approach for the efficient computation of transport and reaction a multispecies multireaction system is developed. The objective this to reduce number coupled nonlinear differential equations drastically, while splitting errors are avoided. reduction mechanism able handle both kinetic reactions heterogeneous equilibrium mobile immobile species. It leads formulation with Jacobian that has very few nonzero entries. Applications networks, including biodegradation problem which...
Modeling carrier‐influenced transport needs to take into account the reactivity of carrier itself. This paper presents a mathematical model reactive solute with sorption mobile and immobile sorbents. The sorbent is also considered be reactive. To justify assumptions generality our modeling approach, experimental findings are reviewed analyzed. A transformation in terms total concentrations sorbents presented which simplifies formulations. Breakthrough data on dissolved organic carbon...
Inverse methods are increasingly used to estimate the hydraulic properties of unsaturated soils. The method generally uses a weighted least-squares approach in which numerically simulated data fitted measured data. In this study we inverse soil from continuous and multistep column outflow experiments. employs piecewise polynomial functions obtain free-form parameterization properties, rather than fixed functional forms typical van Genuchten–Mualem Brooks–Corey–Burdine models. For quadratic...
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 the first part of this article, we extend formal upscaling a diffusion–precipitation model through two-scale asymptotic expansion in level set framework to three dimensions. We obtain upscaled partial differential equations, more precisely, non-linear diffusion equation with effective coefficients coupled equation. As step, consider parametrization underlying pore geometry by single parameter, e.g. generalized “radius” or porosity. Then, transforms an ordinary for parameter. For such...
Abstract Micro‐macro models for dissolution processes are derived from detailed pore‐scale applying upscaling techniques. They consist of flow and transport equations at the scale porous medium (macroscale). Both include averaged time‐ space‐dependent coefficient functions (permeability, porosity, reactive surface, effective diffusion). These in turn explicitly computed geometry unit cells by means auxiliary cell problems defined therein (microscale). The explicit geometric structure is...
In this paper we analyze a fully practical piecewise linear finite element approximation involving numerical integration, backward Euler time discretization, and possibly regularization of the following degenerate parabolic system arising in model reactive solute transport porous media: find $\{u(x,t),v(x,t)\}$ such that \begin{eqnarray*} &\partial_t u + \partial_t v - \Delta =f \quad\mbox{in } \Omega \times(0,T] \qquad u=0\quad\mbox{on \partial\Omega\times(0,T]&\\...