Andriy Sokolov

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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(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(More)
In this paper 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(More)
The paper presents a new discrete projection method for the numerical solution of the Navier-Stokes equations with Coriolis force term. On an algebraic level we interpret one time step of the projection method as an incomplete factorization of the linearized Navier-Stokes system and as the iteration of an Uzawa type algorithm with special preconditioning(More)
For the model-based active control of three-dimensional flows at high Reynolds numbers in real time, low-dimensional models of the flow dynamics and efficient actuator and sensor concepts are required. Numerous successful approaches to derive such models have been proposed in the literature. We propose a software environment for a comfortable and performant(More)
The field-theoretical renormalization group (RG) approach in three dimensions is used to estimate the universal critical values of renormalized coupling constants g6 and g8 for the O(n)-symmetric model. The RG series for g6 and g8 are calculated in the four- and three-loop approximations, respectively, and then resummed by means of the Padé-Borel-Leroy(More)
This paper presents a numerical analysis for complex 3D simulations of the Stirred Tank Reactor (STR) model by a modified discrete projection method (DPM) for rotating incompressible flow. For several proto-typical configurations of the STR model, we examine the multigrid behaviour for the arising momentum and pressure Poisson subproblems for different(More)
The RG functions of the 2D n-vector λφ 4 model are calculated in the five-loop approximation. Perturbative series for the β-function and critical exponents are resummed by the Pade-Borel and Pade-Borel-Leroy techniques, resum-mation procedures are optimized and an accuracy of the numerical results is estimated. In the Ising case n = 1 as well as in the(More)