Stefan Turek | Dortmund University of Technology - Technische Universität Dortmund (original) (raw)

Papers by Stefan Turek

We present an implicit finite element method for a class of chemotaxis models in three spatial di... more We present an implicit finite element method for a class of chemotaxis models in three spatial dimensions. The proposed algorithm is designed to maintain mass conservation and to guarantee positivity of the cell density. To enforce the discrete maximum principle, the standard Galerkin discretization is constrained using a local extremum diminishing flux limiter. To demonstrate the efficiency and robustness of this approach, we solve blow-up problems in a 3D chemostat domain. To give a flavor of more complex and realistic chemotactic applications, we investigate the pattern dynamics and aggregating behavior of the bacteria Escherichia coli and Salmonella typhimurium. The obtained numerical results are in good qualitative agreement with theoretical studies and experimental data reported in the literature.

An implicit flux-corrected transport (FCT) algorithm is deve loped for a class of chemotaxis mode... more An implicit flux-corrected transport (FCT) algorithm is deve loped for a class of chemotaxis models. The coefficients of the Galerkin finite element discretizatio n are adjusted in such a way as to guarantee mass con- servation and keep the cell density nonnegative. The numerical behaviour of the proposed high-resolution scheme is tested on the blow-up problem for a minimal chemotaxis

SIAM Journal on Scientific Computing, 2009

Among a variety of grid deformation methods, the method proposed by Liao [4, is one of the most f... more Among a variety of grid deformation methods, the method proposed by Liao [4, is one of the most favourables, because it prevents mesh tangling and offers precise control over the element volumes. Its numerical realisation only requires solving a Poisson problem and a system of fully decoupled initial value problems. Many other deformation methods in contrast involve the solution of complex nonlinear PDEs. In this article, we introduce a generalisation of Liao's method which allows for generating a desired mesh size distribution for quite arbitrary grids without giving rise to mesh tangling. We elaborate on its numerical realisation and prove the convergence of our method. Our results are confirmed by numerical experiments.

Computational Methods in Applied Mathematics, 2000

An implicit flux-corrected transport (FCT) algorithm is developed for a class of chemotaxis model... more An implicit flux-corrected transport (FCT) algorithm is developed for a class of chemotaxis models. The coefficients of the Galerkin finite element discretization are adjusted in such a way as to guarantee mass conservation and keep the cell density nonnegative. The numerical behaviour of the proposed high-resolution scheme is tested on the blow-up problem for a minimal chemotaxis model with singularities. It is also shown that the results for an Escherichia coli chemotaxis model are in good agreement with experimental data reported in the literature.

Discrete and Continuous Dynamical Systems - Series B, 2013

ABSTRACT We present an implicit finite element method for a class of chemotaxis models, where a n... more ABSTRACT We present an implicit finite element method for a class of chemotaxis models, where a new linearized flux-corrected transport (FCT) algorithm is modified in such a way as to keep the density of on-surface living cells nonnegative. Level set techniques are adopted for an implicit description of the surface and for the numerical treatment of the corresponding system of partial differential equations. The presented scheme is able to deliver a robust and accurate solution for a large class of chemotaxis-driven models. The numerical behavior of the proposed scheme is tested on the blow-up model on a sphere and an ellipsoid and on the pattern-forming dynamics model of Escherichia coli on a sphere.

Nature communications, 2014

Biological microorganisms swim with flagella and cilia that execute nonreciprocal motions for low... more Biological microorganisms swim with flagella and cilia that execute nonreciprocal motions for low Reynolds number (Re) propulsion in viscous fluids. This symmetry requirement is a consequence of Purcell's scallop theorem, which complicates the actuation scheme needed by microswimmers. However, most biomedically important fluids are non-Newtonian where the scallop theorem no longer holds. It should therefore be possible to realize a microswimmer that moves with reciprocal periodic body-shape changes in non-Newtonian fluids. Here we report a symmetric 'micro-scallop', a single-hinge microswimmer that can propel in shear thickening and shear thinning (non-Newtonian) fluids by reciprocal motion at low Re. Excellent agreement between our measurements and both numerical and analytical theoretical predictions indicates that the net propulsion is caused by modulation of the fluid viscosity upon varying the shear rate. This reciprocal swimming mechanism opens new possibilities in...

Computers & Mathematics with Applications, 2012

ABSTRACT In the framework of finite element discretizations, we introduce a fully nonlinear Newto... more ABSTRACT In the framework of finite element discretizations, we introduce a fully nonlinear Newton-like method and a linearized second order approach in time applied to certain partial differential equations for chemotactic processes incorporating two entities, a chemical agent and the reacting population of certain biological organisms/species. We investigate the benefit of a corresponding monolithic approach and the decoupled variant. In particular, we analyze accuracy, efficiency and stability of different methods and their dependences on certain parameters in order to identify a well suited finite element solver for chemotaxis problems.

Computing, 1995

In [7] we proposed a general numerical approach to the (linear) radiative transfer equation which... more In [7] we proposed a general numerical approach to the (linear) radiative transfer equation which resulted in a high-dimensional linear system of equations. Using the concept of the generalized mean intensity, the dimension of the system can be drastically diminished, without losing any information. Additionally, the corresponding system matrices are positive definite under appropriate conditions on the choice of the

Computers & Chemical Engineering, 2011

In this paper, we present numerical techniques for one-way coupling of CFD and Population Balance... more In this paper, we present numerical techniques for one-way coupling of CFD and Population Balance Equations (PBE) based on the incompressible flow solver FeatFlow which is extended with Chien's Low-Reynolds number k-ε turbulence model, and breakage and coalescence closures. The presented implementation ensures strictly conservative treatment of sink and source terms which is enforced even for geometric discretization of the internal coordinate. The validation of our implementation which covers wide range of computational and experimental problems enables us to proceed into three-dimensional applications as, turbulent flows in a pipe and through a static mixer. The aim of this paper is to highlight the influence of different formulations of the novel theoretical breakage and coalescence models on the equilibrium distribution of population, and to propose an implementation strategy for three-dimensional one-way coupled CFD-PBE model.

In this paper multigrid smoothers of Vanka-type are studied in the con- text of Computational Sol... more In this paper multigrid smoothers of Vanka-type are studied in the con- text of Computational Solid Mechanics (CSM).These smoothers were originally de- veloped to solve saddle-point systems arising in the field of Computational Fluid Dynamics (CFD), particularly for incompressible flow problems. When treating (nearly) incompressible solids, similar equation systems arise so that it is reason- able to adopt the 'Vanka

Quadratic and higher order finite elements are interesting candidates for the numerical solution ... more Quadratic and higher order finite elements are interesting candidates for the numerical solution of (elliptic) partial differential equations (PDEs) due to their improved approx- imation properties in comparison to linear approaches. While the systems of equations that arise from the discretisation of the underlying PDEs are often solved by iterative schemes like preconditioned Krylow-space methods, multigrid solvers are still rarely

An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, ... more An Arbitrary Lagrangian-Eulerian (ALE) formulation is applied in a fully coupled monolithic way, considering the fluid-structure interaction (FSI) problem as one continuum. The mathematical description and the numerical schemes are designed in such a way that general constitutive relations (which are realistic for biomechanics applications) for the fluid as well as for the structural part can be easily incorporated. We

Understanding Complex Systems, 2008

Hybrid homogeneous-heterogeneous reactions can arise in catalytic reactions carried out at elevat... more Hybrid homogeneous-heterogeneous reactions can arise in catalytic reactions carried out at elevated temperatures. In this work, hybrid N2O decomposition is investigated at higher temperatures. Unsteady- state processes, such as the periodic flow reversal of fixed-bed reactors have a considerable impact on the way reaction behaviour develops within distributed systems. For the first time, we present a macrokinetic model that incorporates

In this paper we will give a short introduction to the installation and efficiency of state-of-th... more In this paper we will give a short introduction to the installation and efficiency of state-of-the-art direct solver packages like CROUT and UMFPACK for linear systems, combined with highly processor optimised BLAS libraries. We will give an overview about the methods that can be used to integrate these libraries into Fortran programs compiled with the Compaq® Visual Fortran or the

Over the past decades, the field of chemical engineering has witnessed an increased interest in u... more Over the past decades, the field of chemical engineering has witnessed an increased interest in unsteady-state processes. Multifunctional, as well as intensified chemical processes, may exhibit instationary behaviour especially when based on periodical operating conditions. Ideally, instationary processes lead to a higher yield and increased selectivities compared to conventional steady-state fixed-bed processes. Typical candidates among these are the reverse-flow-reactor, the chromatographic reactor and the adsorptive reactor. Since the underlying regeneration strategy is nearly always based on cycles — e.g., a reaction cycle is followed by a regeneration cycle and so on — the overall temporal behaviour of such processes eventually develops into cyclic steady-states (after a transient phase). Experiments reveal a slow transient behaviour into the cyclic steady-state. This can also be observed in simulation based on conventional numerical treatment such as the method of lines. In ad...

thispaper we concentrate on the 2D--case which is representative also for 3D--problems. Relatedre... more thispaper we concentrate on the 2D--case which is representative also for 3D--problems. Relatedresults in 3D can be found in [17].Apart from rather "exotic" schemes like discontinuous space--time Galerkin methods (seeJohnson [9]) and characteristic methods (see Pironneau [13]), the common solution approachis a separate discretization in space and time.2We first (semi-) discretize in time by one of the usual methods known from the treatment of ordinarydifferential equations, such as...