Pavel Strachota

Czech Technical University in Prague | ČVUT · Faculty of Nuclear Sciences and Physical Engineering (FJFI)

This article introduces GTMesh, an open-source C++ library providing data structures and algorithms that facilitate the development of numerical schemes on general polytopal meshes. After discussing the features and limitations of the existing open-source alternatives, we focus on the theoretical description of geometry and the topology of conformi...

Phase field modeling finds utility in various areas. In optimization theory in particular, the distributed control and Neumann boundary control of phase field models have been investigated thoroughly. Dirichlet boundary control in parabolic equations is commonly addressed using the very weak formulation or an approximation by Robin boundary conditi...

As opposed to the distributed control of parabolic PDE's, very few contributions currently exist pertaining to the Dirichlet boundary condition control for parabolic PDE's. This motivates our interest in the Dirichlet boundary condition control for the phase field model describing the solidification of a pure substance from a supercooled melt. In p...

In fluidized bed boilers, the distributor plate is a perforated metal plate which forms the bottom of the combustion chamber and separates it from the windbox. It prevents the fluidized granular material from falling through. At the same time, it allows an even distribution of the fluidization air which flows through the small holes. In this contri...

We investigate a family of phase field models for simulating dendritic growth of a pure supercooled substance. Our aim is to remove limitations inherent to some existing models in terms of the applicability to physically realistic situations and in terms of the possible mathematical and numerical analysis. The central object of interest is the reac...

We present a convergence result for the finite volume method applied to a particular phase field problem suitable for simulation of pure substance solidification. The model consists of the heat equation and the phase field equation with a general form of the reaction term which encompasses a variety of existing models governing dendrite growth and...

This contribution focuses on CFD modeling of the dynamics of the bubbling fluidized bed under conditions specific for oxyfuel combustion. A custom OpenFOAM solver is developed based on the Multiphase Particle-In-Cell framework for handling the fluid-particle and inter-particle interactions. Features of this Euler-Lagrange approach are discussed, an...

We deal with numerical solution of a three-dimensional phase field model of solidification in single component anisotropic materials. In this contribution, we extend the model by crystal orientation transformation. A robust algorithm is then developed to simulate the growth of multiple grains with an arbitrary number of random crystallographic orie...

We propose a novel and efficient numerical approach for solving the pseudo two-dimensional multiscale model of the Li-ion cell dynamics based on first principles, describing the ion diffusion through the electrolyte and the porous electrodes, electric potential distribution, and Butler-Volmer kinetics. The numerical solution is obtained by the fini...

The Allen–Cahn equation originates in the phase field formulation of phase transition phenomena. It is a reaction-diffusion ODE with a nonlinear reaction term which allows the formation of a diffuse phase interface. We first introduce a model initial boundary-value problem for the isotropic variant of the equation. Its numerical solution by the met...

We study the finite-element nonlinear Galerkin method in one spatial dimension and its application to the numerical solution of nontrivial dynamics in selected reaction–diffusion systems. This method was suggested as well adapted for the long-term integration of evolution equations and is studied as an alternative to the commonly used numerical app...

The article provides a brief overview of a one-dimensional model of two-phase flow in the geometry of a circulating fluidized bed combustor exhibiting vertical variability of cross-section. The model is based on numerical solution of conservation laws for mass, momentum and energy of gas and solid components of the fluidized-bed system by means of...

We introduce an outline of the mathematical model of combustion in circulating fluidized bed boilers. The model is concerned with multiphase flow of flue gas, bed material, and two types of fuels (coal and biomass) that can be co-fired in the furnace. It further considers phase interaction resulting in particle attrition, devolatilization and burno...

As an alternative to the sharp interface formulation, the phase field approach is a widely used technique for modeling phase transitions. The governing system of reaction-diffusion equations captures the instability of the underlying physical problem and is capable of modeling the evolution of complicated crystal shapes during solidification of an...

For the purpose of DT-MRI data visualization, an algorithm based on a numerical model of texture diffusion is proposed. As a prerequisite of entering clinical use, its parameters need to be adjusted properly so that the procedure gives satisfactory results with limited computational resources and time available. This contribution introduces the pri...

In the contribution, we summarize results of mathematical modelling and numerical simulation of flow, transport, combustion and reaction processes in industrial stream generators powered by the powderized coal combustion with possible partial biofuel additives (biofuel cofiring). The model is based on numerical solution of conservation laws for mas...

In [15], our DT–MRI visualization algorithm based on anisotropic texture diffusion is introduced. The diffusion is modeled mathematically by the problem for the Allen–Cahn equation with a space–dependent anisotropic diffusion operator. To preserve its anisotropic properties in the discretized version of the problem, an appropriate numerical treatme...

In this contribution, a parallel implementation of the finite volume solver is introduced, designated to numerically solve the initial boundary value problem for the Allen–Cahn equation with anisotropy on large 3D grids. The choice of a suitable numerical scheme is discussed and its convergence properties are investigated by means of evaluation of...

Magnetic Resonance Diffusion Tensor Imaging (MR-DTI) is a noninvasive in vivo method capable of examining the structure of human brain, providing information about the position and orientation of the neural tracts. After a short introduction to the principles of MR-DTI, this paper describes the steps of the proposed neural tract visualization techn...

We propose a method of vector fleld visualization based on noisy texture smearing. The smearing process is carried out by solving the Allen-Cahn equation with advection. We state the theorem of existence and uniqueness of the weak solution and derive the appropriate a priori estimate. The numerical algorithm for PDE solution is introduced together...

This contribution discusses two attitudes to artificial dissipation reduction in numer-ical schemes for solving initial boundary value problems for the Allen-Cahn equation with anisotropy incorporated into the diffusion operator. In the first case, a weighted first order finite difference scheme is used for spatial discretization of the anisotropic...

In the course of tuning the developed numerical algorithm for MR-DTI data visual-ization, it was necessary to introduce a measurement technique capable of quantitatively assessing the artificial isotropic diffusion in numerical schemes for PDE. Based on such assessment, a qualified choice of the numerical scheme can be made. This contribution descr...

We propose a method of vector field visualization based on noisy texture smearing. The smearing process is carried out by solving a problem for the Allen-Cahn diffusion PDE with advection. We introduce a parallel algorithm for the numerical solution of the given problem and we present several results of the efficiency benchmark. Finally, an extensi...

We present a numerical study of flow in a 2D chamber of a simplified industrial boiler. The study features multiple cases of flow with different inlet settings. The mathematical model is based on the incompressible Navier-Stokes equations and solved numerically by means of finite element method. The time discretization is semi-implicit and the resu...