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Search results for: MULTI-EQUATION MODELS
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Modelling of FloodWave Propagation with Wet-dry Front by One-dimensional Diffusive Wave Equation
PublicationA full dynamic model in the form of the shallow water equations (SWE) is often useful for reproducing the unsteady flow in open channels, as well as over a floodplain. However, most of the numerical algorithms applied to the solution of the SWE fail when flood wave propagation over an initially dry area is simulated. The main problems are related to the very small or negative values of water depths occurring in the vicinity of...
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ADAPTIVE METHOD FOR THE SOLUTION OF 1D AND 2D ADVECTION-DIFFUSION EQUATIONS USED IN ENVIRONMENTAL ENGINEERING
PublicationThe paper concerns the numerical solution of one-dimensional (1D) and two-dimensional (2D) advection-diffusion equations. For the numerical solution of the 1D advection-diffusion equation a method, originally proposed for solution of the 1D pure advection equation, has been developed. A modified equation analysis carried out for the proposed method allowed increasing of the resulting solution accuracy and consequently, to reduce...
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Elastic scattering of electrons by water: An ab initio study
PublicationIn this work we devise a theoretical and computational method to compute the elastic scattering of electrons from a non-spherical potential, such as in the case of molecules and molecular aggregates. Its main feature is represented by the ability of calculating accurate wave functions for continuum states of polycentric systems via the solution of the Lippmann-Schwinger equation, including both the correlation effects and multi-scattering...
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Analyses of Shear Angle in Orthogonal Cutting of Pine Wood
PublicationThe determination of energy effects for wood machining processes, such as cutting power and cutting forces, is very useful in designing of manufacture process of wooden products. A more accurate prediction of cutting forces requires a correct determination of the shear angle value, which can be determined using various models. In this article, shear angle values for an orthogonal linear cutting process of pine wood are determined. The...
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Minimal parameter implicit solvent model for ab initioelectronic-structure calculations
PublicationAbstract - We present an implicit solvent model for ab initio electronic-structure calculations which is fully self-consistent and is based on direct solution of the nonhomogeneous Poisson equation. The solute cavity is naturally defined in terms of an isosurface of the electronic density according to the formula of Fattebert and Gygi (J. Comput. Chem., 23 (2002) 662). While this model depends on only two parameters, we demonstrate...
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Ruch wirowy wywoływany przez ultradźwięk w płynach z relaksacją
PublicationRozprawa doktorska poświęcona jest badaniu ruchu wirowego wywoływanego przez ultradźwięk w różnych modelach płynów z relaksacją. Ma ona charakter teoretyczny, jednak wykorzystanie uzyskanych dzięki niej wyników może przynieść lepsze zrozumienie ruchu wirowego wywoływanego przez siłę akustyczną. W I rozdziale rozprawy przedstawione zostały ogólne rozważania dotyczące akustyki nieliniowej. Rozdział II dotyczy ruchu wirowego wywoływanego...
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Torsional buckling and post-buckling of columns made of aluminium alloy
PublicationThe paper concerns torsional buckling and the initial post-buckling of axially compressed thin-walled aluminium alloy columns with bisymmetrical cross-section. It is assumed that the column material behaviour is described by the Ramberg–Osgood constitutive equation in non-linear elastic range. The stationary total energy principle is used to derive the governing non-linear differential equation. An approximate solution of the equation...
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Numerical Simulations and Tracer Studies as a Tool to Support Water Circulation Modeling in Breeding Reservoirs
PublicationThe article presents a proposal of a method for computer-aided design and analysis of breeding reservoirs in zoos and aquariums. The method applied involves the use of computer simulations of water circulation in breeding pools. A mathematical model of a pool was developed, and a tracer study was carried out. A simplified model of two-dimensional flow in the form of a biharmonic equation for the stream function (converted into...
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The finite-difference simulation of x-rays propagation through a system of lenses
PublicationThe propagation of X-ray waves through an optical system consisting of 33 aluminum X-ray refractive lenses is considered. For solving the problem, a finite-difference method is suggested and investigated. It is shown that very small steps of the difference grid are necessary for reliable computation of propagation of X-ray waves through the system of lenses. It is shown that the wave phase is a function very quickly increasing...
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Entropy Production Associated with Aggregation into Granules in a Subdiffusive Environment
PublicationWe study the entropy production that is associated with the growing or shrinking of a small granule in, for instance, a colloidal suspension or in an aggregating polymer chain. A granule will fluctuate in size when the energy of binding is comparable to k_{B}T, which is the “quantum” of Brownian energy. Especially for polymers, the conformational energy landscape is often rough and has been commonly modeled as being self-similar...
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Acoustic heating produced in resonators filled by a newtonian fluid
PublicationAcoustic heating in resonators is studied. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in the linear part of the final equation, but preserving terms belonging to the thermal mode responsible for heating. This equation is instantaneous and includes nonlinear acoustic terms that form a...
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Balance errors generated by numerical diffusion in the solution of non-linear open channel flow equations
PublicationThe paper concerns the untypical aspect of application of the dissipative numerical methods to solve nonlinear hyperbolic partial differential equations used in open channel hydraulics. It is shown that in some cases the numerical diffusion generated by the applied method of solution produces not only inaccurate solution but as well as a balance error. This error may occur even for an equation written in the conservative form not...
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Impact of Boundary Conditions on Acoustic Excitation of EntropyPerturbations in a Bounded Volume of Newtonian Gas
PublicationExcitation of the entropy mode in the field of intense sound, that is, acoustic heating, is theoreticallyconsidered in this work. The dynamic equation for an excess density which specifies the entropy mode,has been obtained by means of the method of projections. It takes the form of the diffusion equation withan acoustic driving force which is quadratically nonlinear in the leading order. The diffusion coefficient isproportional...
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Numerical simulation of cold flow and combustion in a swirl stabilized combustor
PublicationA numerical simulation model was developed to investigate the cold flow and combustion using Ansys FLUENT 2021R1. The governing equations were solved using the pressure-based method, and pressure–velocity coupling was performed using the SIMPLE method. To model the turbulent process, the RSM model was used. Non-premixed model is chosen to solve the chemical kinetics between fuel and oxigen. Radiation heat transfer was calculated...
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On the Buckling Response of Axially Pressurized Nanotubes Based on a Novel Nonlocal Beam Theory
PublicationIn the present study, the buckling analysis of single-walled carbon nanotubes (SWCNT) on the basis of a new refined beam theory is analyzed. The SWCNT is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new proposed beam theory has only one unknown variable which leads to one equation similar to Euler beam theory and is also free from any shear correction factors. The equilibrium...
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Sustainable energy consumption – Empirical evidence of a household in Poland
PublicationThere is an expected increase in the demand for electricity from households in European countries. The outcome of the growing proportion of renewable energy sources in the energy supply mix should result in improved customer awareness regarding their electricity usage. Additionally, they must assume a more proactive role in overseeing their electricity usage. Innovation and pollution management have become crucial catalysts for...
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On various modelling approaches to real-time visualisation of blood flow
PublicationThis paper reviews various modelling approaches to real-time visualisation of blood flow. These include classic, macroscale approach based on the momentum conservation equation together with a proper constitutive equation. Moreover, modern micro- and mesoscale approaches, such as molecular dynamics and dissipative particle dynamics, are discussed. Advantages and disadvantages of the discussed methods are highlighted with particular...
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Vortex flow caused by periodic and aperiodic sound in a relaxing maxwell fluid
PublicationThis paper concerns the description of vortex flow generated by periodic and aperiodic sound in relaxing Maxwell fluid. The analysis is based on governing equation of vorticity mode, which is a result of decomposition of the hydrodynamic equations for fluid flow with relaxation and thermal conductivity into acoustical and non-acoustical parts. The equation governing vorticity mode uses only instantaneous, not averaged over sound...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublicationIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which leads to one equation similar to the Euler beam theory and also is free of any shear correction factor. The equilibrium equation has been...
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On forced vibrations of piezo-flexomagnetic nano-actuator beams
PublicationThe effect of excitation frequency on the piezomagnetic Euler-Bernoulli nanobeam taking the flexomagnetic material phenomenon into consideration is investigated in this chapter. The magnetization with strain gradients creates flexomagneticity. We couple simultaneously the piezomagnetic and flexomagnetic properties in an inverse magnetization. Resemble the flexoelectricity, the flexomagneticity is also size-dependent. So, it has...
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Flexomagnetic response of buckled piezomagnetic composite nanoplates
PublicationIn this paper, the equation governing the buckling of a magnetic composite plate under the influence of an in-plane one-dimensional magnetic field, assuming the concept of flexomagnetic and considering the resulting flexural force and moment, is investigated for the first time by different analytical boundary conditions. To determine the equation governing the stability of the plate, the nonlocal strain gradient theory has been...
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Acoustic heating produced in the boundary layer
Publication: Instantaneous acoustic heating of a viscous fluid flow in a boundary layer is the subject of investigation. The governing equation of acoustic heating is derived by means of a special linear combination of conservation equations in the differential form, which reduces all acoustic terms in the linear part of the final equation but preserves terms belonging to the thermal mode. The procedure of decomposition is valid in a weakly...
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Flood Modelling and Risk Analysis of Cinan Feizuo Flood Protection Area, Huaihe River Basin
PublicationThis study evaluated multiple aspects of flood risks and effects on the Cinan Feizuo flood protection area in the Huaihe River basin. Flooding remains a leading problem for infrastructure, especially in urban, residential areas of the region. Effective flood modeling for urbanized floodplains is challenging, but MIKE (ID-2D) is paramount for analyzing and quantifying the risk in the vulnerable region. The Saint-Venant equation...
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Coupled Urban Areas Inundation Model with Interaction Between Storm Water System and Surface Flow - Case Study of Sea Level Impact on Seaside Areas Flooding
PublicationInundations are becoming more frequent than ever. What is connected with increasing area of impervious surface in cities. This makes predicting urban flooding and its scale especially important. At the seaside we observe additional conditions such as sea level that makes accurate numerical modelling of issue even harder. With complex approach to the matter which is simultaneous calculation of storm water conduit flow and overland...
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Impact of Usability Website Attributes on Users’ Trust, Satisfaction and Loyalty
PublicationThis paper presents the results of an experimental study aimed at identifying possible relationships among website usability characteristics, consumer satisfaction, trust and loyalty. These factors regard not only customer satisfaction in a transactional sense, but in the long term they may affect e-customer behavior, opinions, recommendations and attitudes toward using on-line services in general. The study was performed with...
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Mathematical Modeling of the Impact Range of Sewage Discharge on the Vistula Water Quality in the Region of Włocławek
PublicationThe paper presents results of analysis of the industrial sewage discharge influence at km 688 + 250 of the Vistula River on water quality. During the analysis, two-dimensional models of flow, impurities and temperature transport were used. Hydrological conditions of the analyzed section of the river, characteristic flows and bathymetry of the riverbed in the first instance were defined. Calculations of velocity distribution at...
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Performance assessment of OpenMP constructs and benchmarks using modern compilers and multi-core CPUs
PublicationConsidering ongoing developments of both modern CPUs, especially in the context of increasing numbers of cores, cache memory and architectures as well as compilers there is a constant need for benchmarking representative and frequently run workloads. The key metric is speed-up as the computational power of modern CPUs stems mainly from using multiple cores. In this paper, we show and discuss results from running codes such as:...
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Acoustic heating produced in the thermoviscous flow of a Bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Temperature-dependent structure-property modeling of viscosity for ionic liquids
PublicationIn this paper we present the methodology for assessing the ionic liquids' viscosity at six temperature points (25, 35, 45, 50, 60 and 70 [C]), which utilizes only the in silico approach. The main idea of such assessment is based on the "correction equation" describing the correlation between experimentally measured viscosity and theoretically derived density (calculated with use of molecular mechanics), given at 6 different temperature...
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Efficiency of acoustic heating produced in the thermoviscous flow of a fluid with relaxation
PublicationInstantaneous acoustic heating of a fluid with thermodynamic relaxation is the subject of investigation. Among others, viscoelastic biological media described by the Maxwell model of the viscous stress tensor, belong to this type of fluid. The governing equation of acoustic heating is derived by means of the special linear combination of conservation equations in differential form, allowing the reduction of all acoustic terms in...
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Acoustic heating produced in the thermoviscous flow of a bingham plastic
PublicationThis study is devoted to the instantaneous acoustic heating of a Bingham plastic. The model of the Bingham plastic's viscous stress tensor includes the yield stress along with the shear viscosity, which differentiates a Bingham plastic from a viscous Newtonian fluid. A special linear combination of the conservation equations in differential form makes it possible to reduce all acoustic terms in the linear part of of the final equation...
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Examples of numerical simulations of two-dimensional unsaturated flow with VS2DI code using different interblock conductivity averaging schemes
PublicationFlow in unsaturated porous media is commonly described by the Richards equation. This equation is strongly nonlinear due to interrelationships between water pressure head (negative in unsaturated conditions), water content and hydraulic conductivity. The accuracy of numerical solution of the Richards equation often depends on the method used to estimate average hydraulic conductivity between neighboring nodes or cells of the numerical...
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Influence of heterogeneous air entry pressure on large scale unsaturated flow in porous media
PublicationThe paper presents numerical simulations of water infiltration in unsaturated porous media containing coarse-textured inclusions embed- ded in fine-textured background material. The calculations are performed using the two-phase model for water and air flow and a simplified model known as the Richards equation. It is shown that the Richards equation cannot correctly describe flow in the presence of heterogeneities. How- ever, its...
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Numerical modelling and experimental verification of compressible squeeze film pressure
PublicationThe validity of using the Reynolds equation for compressible squeeze film pressure was tested with computational fluid dynamics (CFD). A squeeze film air bearing was instrumented with pressure sensors and non-contacting displacement probes to provide transient measurements of film thickness and pressure. The film thickness measurements also provided input parameters to the numerical prediction. However, numerical results showed...
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Analytical Buckling of FG Nanobeams on The Basis of A New One Variable First-Order Shear Deformation Beam Theory
PublicationIn this work, buckling analysis of functionally graded (FG) nanobeams based on a new refined beam theory has been analyzed. The beam is modeled as an elastic beam subjected to unidirectional compressive loads. To achieve this aim, the new obtained beam theory has only one variable which lead to one equation similar to Euler beam theory and also is free of any shear correction factor. The...
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Improvement of Thrust Bearing Calculation Considering the Convectional Heating within the Space between the Pads
PublicationA modern thrust bearing tool is used to estimate the behavior of tilting pad thrust bearings not only in the oil film between pad and rotating collar, but also in the space between the pads. The oil flow in the space significantly influences the oil film inlet temperature and the heating of pad and collar. For that reason, it is necessary to define an oil mixing model for the space between the pads. In the bearing tool, the solutions...
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Wear of electroplated diamond tools in lap-grinding of Al2O3 ceramic materials
PublicationCurrent development of modern products, together with ever-increasing demands for their operation and usage, necessitate the search for new processing methods. Abrasive machining is widely used in many industrial areas, especially for processing difficult-to-machine materials such as advanced ceramics. Grinding with lapping kinematics, also called lap-grinding, is still one of the innovative methods of abrasive processing being...
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Prognozowanie właściwości złączy spawanych pod wodą metodą lokalnej komory suchej
PublicationNiniejsza praca jest poświęcona spawaniu pod wodą metodą lokalnej komory suchej (MLKS) i przedstawia metodologię oraz narzędzia umożliwiające prognozowanie właściwości złączy spawanych wykonanych przy zastosowaniu tej odmiany spawania. Monografia zawiera opis rozwoju spawania pod wodą oraz charakterystykę metod wykorzystywanych do realizacji prac spawalniczych. Zaproponowano nowy podział metod spawania pod wodą, uwzględniający...
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DL_MG: A Parallel Multigrid Poisson and Poisson–Boltzmann Solver for Electronic Structure Calculations in Vacuum and Solution
PublicationThe solution of the Poisson equation is a crucial step in electronic structure calculations, yielding the electrostatic potential -- a key component of the quantum mechanical Hamiltonian. In recent decades, theoretical advances and increases in computer performance have made it possible to simulate the electronic structure of extended systems in complex environments. This requires the solution of more complicated variants of the...
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On local buckling of cold-formed channel members
PublicationThe paper deals with local buckling of the compressed flanges of cold-formed thin-walled channel beams subjected to pure bending or axially compressed columns. Arbitrarily shaped flanges of open cross-sections and the web-flange interactions are taken into account. Buckling deformation of a beam flange is described by displacement related to torsion of the flange about the line of its connection with the web. Total potential energy...
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ESTIMATING AVERSION TO RANK INEQUALITY UNDERLYING SELECTED ITALIAN INDICES OF INCOME INEQUALITY
PublicationIn this paper, we estimate aversion to rank inequality (ATRI) underlying selected Italian income inequality indices, I, notably the Pietra index, the Bonferroni index and the “new” Zenga index. We measure ATRI by the parameter v of the generalised Gini index G(v). ATRI is distinct from aversion to income inequality, as measured by parameter ε of Atkinson’s index A(ε). We propose eliciting v from the equation I = GE(v). As, in general,...
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Mountain pass solutions to Euler-Lagrange equations with general anisotropic operator
PublicationUsing the Mountain Pass Theorem we show that the problem \begin{equation*} \begin{cases} \frac{d}{dt}\Lcal_v(t,u(t),\dot u(t))=\Lcal_x(t,u(t),\dot u(t))\quad \text{ for a.e. }t\in[a,b]\\ u(a)=u(b)=0 \end{cases} \end{equation*} has a solution in anisotropic Orlicz-Sobolev space. We consider Lagrangian $\Lcal=F(t,x,v)+V(t,x)+\langle f(t), x\rangle$ with growth conditions determined by anisotropic G-function and some geometric conditions...
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Biomass estimation using a length-weight relationship in beetle larvae (Coleoptera: Aphodiidae, Histeridae, Hydrophilidae, Staphylinidae) obtained from cow dung
PublicationThis research enabled the relationship between length and dry body mass to be determined for 158 beetle larvaetaken from cow dung in north-eastern Poland. The larvae were divided into three morphological types, for which the power and linear function of the body length-weight relationship were determined. The linear regression equation characterizes the relationship between body weight and...
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Efficiency of acoustic heating in the Maxwell fluid
PublicationThe nonlinear effects of sound in a fluid describing by the Maxwell model of the viscous stress tensor is the subject of investigation. Among other, viscoelastic biological media belong to this non-newtonian type of fluids. Generation of heating of the medium caused by nonlinear transfer of acoustic energy, is discussed in details. The governing equation of acoustic heating is derived by means of the special linear combination...
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Subcritical bifurcation of free elastic shell of biological cluster
PublicationIn this paper we will investigate symmetry-breaking bifurcation of equilibrium forms of biological cluster. A biological cluster is a two-dimensional analogue of a gas balloon. The cluster boundary is connected with its kernel by elastic links. The inside part is filled with compressed gas or fluid. Equilibrium forms of biological cluster can be found as solutions of a certain second order ordinary functional-differential equation...
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Influence of the air phase on water flow in dikes
PublicationNumerical models are often used to describe flow and deformation processes occurring in dikes during flood events. Modeling of such phenomena is a challenging task, due to the complexity of the system, consisting of three material phases: soil skeleton, pore water and pore air. Additional difficulties are transient loading caused by variable in time water levels, heterogeneity of the soil or air...
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Thermodynamic Characteristics of Phenacetin in Solid State and Saturated Solutions in Several Neat and Binary Solvents
PublicationThe thermodynamic properties of phenacetin in solid state and in saturated conditions in neat and binary solvents were characterized based on differential scanning calorimetry and spectroscopic solubility measurements. The temperature-related heat capacity values measured for both the solid and melt states were provided and used for precise determination of the values for ideal solubility, fusion thermodynamic functions, and...
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Theory versus experiment for vacuum Rabi oscillations in lossy cavities. II. Direct test of uniqueness of vacuum
PublicationThe paper continues the analysis of vacuum Rabi oscillations we started in part I [Phys. Rev. A 79, 033836 (2009)]. Here we concentrate on experimental consequences for cavity QED of two different classes of representations of harmonic-oscillator Lie algebras. The zero-temperature master equation, derived in part I for irreducible representations of the algebra, is reformulated in a reducible representation that models electromagnetic...
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Hyperbolic heat conduction at a microscopic sliding contact with account of adhesion-deformational heat generation and wear
PublicationDifferent non-Fourier models were proposed to simulate temperatures in materials subjected to extremely fast thermal disturbances, when the speed of heat propagation should be concerned. The present study investigated temperature and heat balance at a microscopic sliding contact during a single frictional interaction based on the Cattaneo-Vernotte hyperbolic heat conduction equation. Two fundamental features of friction, namely,...