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In the thin airfoil theory, the camber line and the thickness distribution of general airfoils are mainly extracted by a linear combination of the upper and lower surfaces, giving rise to geometric distortions at the leading edge. Furthermore, despite the recent effort to obtain analytic expressions for the zero-lift angle of attack and quarter-chord moment coefficient, analytic generalizations are needed for the camber line component in the trigonometric series coefficients. In this sense, the present paper proposes a straightforward algorithm to extract the camber line and thickness distribution of general-shaped airfoils based on a finite difference method and the Bézier curve fitting. Integrals in the thin airfoil theory involving a Bernstein basis are performed, leading to series coefficients related to Gegenbauer polynomials. The algorithm is validated against analytical expressions of the NACA airfoils without introducing or adapting geometric parameters, and the results demonstrate good accuracy. In addition, the proposed algorithm indicated a significantly different geometric behavior for the SD7003 and E387 airfoils' camber slope at the leading edge in contrast with the classical linear approximation. Moreover, the method can be coupled conveniently in recent unsteady aerodynamic models established on the thin airfoil theory to obtain closed-form expressions for general airfoils. [ABSTRACT FROM AUTHOR]

Micrometer-scale holes were created on the plate of poly(methyl methacrylate)-PMMA with a carbon dioxide laser. The resulting holes were examined, and mathematical modeling of the formation of the holes was made. The Fourier finite difference and then the least-squares method were used to model the heat dissipation along the line on the PMMA surface. Fourier finite difference and least squares methods were used to examine the effect of laser beam power on the dimensions of the laser-produced hole and to model the heat dissipation. Thermo-physical properties of PMMA, such as heat transfer coefficient and absorption coefficient, were also taken into account and used in the modeling. Before creating the mathematical model, firstly, a laser beam with a power of 52 W was applied to the polymer material. The numerical values obtained as a result of the measurements made with the cavity that was created with laser were used in the proposed mathematical model. Then, the cavity was created using a lower laser power (39 W) to prove that the mathematical model is suitable mathematical model. Measurements were made on the cavity obtained, and the results obtained with the model were compared. Similarly, to prove the reliability of the model, two more cavities were created using two higher laser power (65 and 78 W). Measurements were made on these cavities, and the results were compared with the results obtained with the mathematical model. It has been reported that the experimental results and the results obtained with the mathematical model are in agreement. [ABSTRACT FROM AUTHOR]

This work is concerned with the implementation of a decoupled diffuse interface approach for the numerical solution of two‐phase flows with a moving interface. The underlying two‐phase flow model consists of a mass‐preserving Cahn–Hilliard (CH) equation coupled with the incompressible Navier–Stokes equations (NSEs) through surface tension. Due to the higher order nonlinearity and stiff nature of the CH equation, its numerical solution is very challenging. We have used the decoupled pressure projection method for the numerical simulation of the governing equations. The spatial variables are discretized using the finite difference scheme on the staggered grids, while the explicit Euler method is used for time discretization. Four examples include the coalescence of inline rising bubbles, the obliques coalescence of two rising bubbles, and the deformation of single and two different‐sized bubbles in a shear flow field is numerically simulated. It is observed that the scheme is capable of tracking the interface accurately and respecting mass conservation and energy dissipation. Moreover, the scheme is efficient, easily implementable, energy stable, and fully decoupled. [ABSTRACT FROM AUTHOR]

We present a simple nonlinear model of a shear-beam building that experiences large nonlinear deformations and collapse when excited by large pulses of strong earthquake ground motion. In this paper, we introduce the model and show that its properties can be selected to be consistent with the damage observed in a seven-story hotel in San Fernando Valley of the Los Angeles metropolitan area during the 1994 Northridge earthquake. We also show an example of excitation that leads to the collapse of the model. We illustrate the response only for a sequence of horizontal pulses. We will describe the response of the same model to horizontal, vertical, and rocking motions at its base, as well as for more general excitation by strong earthquake ground motion, in future papers.

We present a simple nonlinear model of a shear-beam building that experiences large nonlinear deformations and collapse when excited by large pulses of strong earthquake ground motion. In this paper, we introduce the model and show that its properties can be selected to be consistent with the damage observed in a seven-story hotel in San Fernando Valley of the Los Angeles metropolitan area during the 1994 Northridge earthquake. We also show an example of excitation that leads to the collapse of the model. We illustrate the response only for a sequence of horizontal pulses. We will describe the response of the same model to horizontal, vertical, and rocking motions at its base, as well as for more general excitation by strong earthquake ground motion, in future papers. [ABSTRACT FROM AUTHOR]

The flow and heat characteristics of an unsteady, laminar biomagnetic fluid, namely blood containing Fe3O4 magnetic particles, under the influence of thermal radiation and a magnetic dipole over a cylinder with controlled boundary conditions using a group theory method are investigated in the present study. The mathematical formulation of the problem is constructed with the aid of biomagnetic fluid dynamics (BFD) which combines principles of ferrohydrodynamics (FHD) and magnetohydrodynamics (MHD). It is assumed that blood exhibits polarization as well as electrical conductivity. Additionally, the shape of the magnetic particles, namely cylindrical and spherical, is also considered. Moreover, in this model, a group theoretical transformation, namely a two-parameter group technique, is applied. By applying this group transformation, the governing system of partial differential equations (PDEs) along with applicable boundary conditions are reduced to one independent variable and, consequently, converted into a system of ordinary differential equations (ODEs) with suitable boundary conditions. An efficient numerical technique is applied to solve the resultant ODEs and this technique is based on three essential features, namely (i) a common finite differences method with central differencing, (ii) tridiagonal matrix manipulation and (iii) an iterative procedure. The flow and heat characteristics of blood-Fe3O4 are found to be dependent on some physical parameters such as the particle volume fraction, the ferromagnetic interaction parameter, the magnetic field parameter, and the thermal radiation parameter. An ample parametric study is accomplished to narrate the influences of such physical parameters on velocity, temperature distributions as well as the coefficient of skin friction and rate of heat transfer. From the numerical results, it is deduced that the fluid velocity is enhanced for the ferromagnetic number and the temperature profile is decreased as the ferromagnetic number is gradually increased. It is also obtained that for the cylindrical shape of magnetic particles, the fluid temperature is more enhanced than that of the spherical shape. Both the skin friction coefficient and the local Nusselt number are increased for increasing values of the ferromagnetic interaction parameter, where the heat transfer rate of blood-Fe3O4 is significantly increased by approximately 33.2% compared to that of pure blood, whereas the coefficient of skin friction is reduced by approximately 6.82%. [ABSTRACT FROM AUTHOR]

Within the FOR3010 Refrabund project, a new type of composite refractory consisting of alumina and refractory metals such as tantalum and niobium is developed. This material is characterized by its ability to conduct electricity, which offers new opportunities for functional parts in high‐temperature environments. To support the development of material properties and production technology, a new simulation approach is needed, which is able to describe irregularly shaped particles of at least two different phases. Current simulations of sintering processes work often with heavily idealized powder geometries. As sintering is mainly driven by gradients of chemical potential due to surface curvatures, a realistic description of the particle geometry is essential for achieving precise simulation results. Herein, a new approach of modeling the sintering behavior of irregularly shaped powder particles by the use of a finite differences approach is developed. A discrete description of irregular powder particles is introduced, and the diffusional flows at their surfaces and sintering necks as well as their development in time are calculated. The new model is compared with an older model using spherical particle geometries from literature. Comparison with experimental results follows in a subsequent publication. [ABSTRACT FROM AUTHOR]

The present study deals with numerical simulation of a typical flat plate solar collector. The transient two-dimensional governing differential equations of absorber plate, working fluid and glass cover were formulated to describe the thermal problem of the collector. The governing differential equations were solved numerically using Finite Differences Method and the transient problem was formulated using implicit scheme which gives a stable solution for any grid size and time step. The two-dimensional temperature distribution in absorber plate was achieved at 2211 nodes at every 10 s of the simulation period that extended for 1800 s. The variation of fluid exit temperature and glass cover temperature were also estimated. The estimation of top heat loss coefficient and collector efficiency becomes possible using the temperature distributions of absorber plate and working fluid along with cover temperature. The variations of mean plate temperature, fluid exit temperature, cover temperature, top heat loss coefficient and collector efficiency were drawn during the simulation period. Temperature distribution contours were also drawn at selected time intervals and irradiance values. It was concluded that the top heat loss coefficient of the solar collector is a strong function of the irradiance and working fluid mass flow rate. Increasing the value of mass flow rate shortened the transient period of the solar collector and rendered the transient curves of the collector parameters more flat. The study can be useful for further understanding the complex transient two-dimensional thermal problem occurring in flat plate solar collectors.

In the course of the documentation works aimed at updating exploitable resources of the groundwater intake, an unexpected change in hydrodynamic field arrangement was observed in a fragment of the area. In relation to the observations made so far, lasting several decades, the groundwater table switched its slope, indicating the flow in the opposite direction than originally. Initially, in the range of the surveyed hydrogeological structure, no object was identified whose draining character could cause such an effect. No significant groundwater extraction or drainage points were documented within a radius of several kilometers. It was only the extended scope of spatial analysis that made it possible to identify the probable cause of a local change in the water table position as a mining pit located in the neighboring hydrogeological structure. The two adjacent hydrogeological structures treated separately so far revealed an experimentally confirmed hydraulic connection. An in-depth analysis of the problem showed the necessity of modifying the existing model of the structure in order to map the observed interactions. An additional simulation module of General-Head Boundary type was applied. The quantity of lateral groundwater exchange between two hydrogeological structures was estimated using mathematical modeling at 3.4 thousand m3/d (reconstructed current state, after model calibration). Further work should aim at treating reservoirs as hydraulically connected after exceeding limiting parameters. [ABSTRACT FROM AUTHOR]

From the implementation of analytical solutions for thin rectangular slabs using the Finite Difference Method, the present paper was developed with the purpose of comparing the determined efforts in a concrete plate with those that would be found using the tables originated from the plates theory of authors established in the literature. For this, the programming language Python was used, taking as a case study, a slab with dimensions of 5 meters long by 3 meters wide and thickness equal to 0.10 meters. In the analysis of the efforts, several support conditions were considered, in which the internal efforts and displacements obtained by the Finite Difference Method were compared with the results obtained through the tables proposed in literature. It was verified that the Finite Difference Method constitutes a good alternative for the resolution of thin solid plates, since the results were similar to the classic solution proposed in literature. The implemented program allows the visualization of the efforts through of spectrums of zone which facilitates the understanding of the distribution of the efforts along the slab, differing slightly from the uniform distribution adopted in the tables consulted.

Copyright of Baghdad Science Journal is the property of Republic of Iraq Ministry of Higher Education & Scientific Research (MOHESR) and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This wok focuses to develop a numerical computation program allowing to design new contours of a supersonic nozzle having several bells, adapted to several levels of different altitudes, going from sea level and progressively with the altitude up to space, giving a supersonic uniform and parallel flow to the exit section and a maximum possible thrust without loss, aiming to reduce considerably the side loads caused in the conventional and the dual bell nozzles when the ambient pressure decrease with the altitude. The first bell has a sonic, uniform and parallel inlet to the throat, and a sea level adaptation with a reduced supersonic Mach number, while the other bell have a supersonic, parallel and uniform inlet and an adaptation to a given altitude with a progressed increase of supersonic Mach number. The transition from one level of adaptation to another adjacent is done without mechanical activation. The purpose of this type of nozzle is to have the possibility of flying in several supersonic regimes adapted to several different altitudes with a reduced side loads. This type of nozzle is named by Several Bell Nozzle and has inflection points between bell and adjacent other. The design is done in the context of a calorically and thermally perfect gas. The problem is to design a typical bell having a uniform and parallel supersonic inlet and exit with two given Mach numbers. The design is made by the use of the Method of Characteristics. The resolution of the equations is done numerically by the finite difference corrector predictor algorithm. The validation of the results is controlled by the convergence of the ratio of the critical sections, calculated numerically, to that given by the theory. In this case, all the design parameters converge automatically to the desired solution. The application is made for axisymmetric MLN having 3, 4, 5 and 10 bells. [ABSTRACT FROM AUTHOR]

The temperature of annealed steel coils is a determining variable of future steel sheets quality. This variable also determines the energy consumption in operation. Unfortunately, the monitoring of coil inner temperature is problematic due to the furnace environment with high temperature, coil structure, and annealing principle. Currently, there no exist measuring principles that can measure the temperature inside the heat-treated product in a non-destructive manner. In this paper, the soft sensing of inner temperature based on the theory of non-stationary heat conduction and approach based on Support Vector Regression (SVR) is presented. The results showed that a black-box approach based on the SVR could replace an analytic approach though with less performance. Several annealing experiments were performed to create a training data set and model performance improvement in the estimation of inner coil temperatures. The proposed software-based on nonstationary heat conduction can calculate the behavior of inner coil temperature from the measured boundary temperatures that are measured by thermocouples. Soft-sensing principles presented in this paper were verified in laboratory conditions and on data obtained from real annealing plant.

Copyright of Radio Electronics, Computer Science, Control is the property of Zaporizhzhia National Technical University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The aim of this study is to present a general model with variable coefficients corresponding to some structural elements such as beam, string, bar, and rod. To solve general model with variable coefficients, a different solution procedure combining a method of multiple scales (MMS) and a finite difference method (FDM) is presented in this study. This technique provides an advantage in the numerical solution of the structural element model containing any discontinuity and in its dynamical analysis by perturbation method. Furthermore, two problems including discontinuity are considered to show the accuracy of the method presented. The comparisons of the numerical results obtained from the proposed method and classical method are introduced. [ABSTRACT FROM AUTHOR]

In the current investigation, the transport of nanoparticles in porous medium is described in a general way. The main objective of this study is the resolution of the equation that governs the transport and the performance of the nanoparticles along their path through the porous media. It is essential to highlight the significant role of nanoparticles at a present time, using vital and multidisciplinary uses. Especially in the field of sanitary-engineering nanoparticles possess a very vital usage that allows reducing the concentration of different contaminants in water. Various characteristics associated with the properties of nanoparticles in relation to the porous media are presented in this study. Relying upon the concepts developed, a mathematical equation is proposed to analyze the transport and behavior of the transport of nanoparticles in porous media. The finite differences method is utilized, and a computational model is developed using MATLAB program. The theoretical outcomes verified that the results and graphs obtained are satisfactory and comply with what was expected.

In the course of the documentation works aimed at updating exploitable resources of the groundwater intake, an unexpected change in hydrodynamic field arrangement was observed in a fragment of the area. In relation to the observations made so far, lasting several decades, the groundwater table switched its slope, indicating the flow in the opposite direction than originally. Initially, in the range of the surveyed hydrogeological structure, no object was identified whose draining character could cause such an effect. No significant groundwater extraction or drainage points were documented within a radius of several kilometers. It was only the extended scope of spatial analysis that made it possible to identify the probable cause of a local change in the water table position as a mining pit located in the neighboring hydrogeological structure. The two adjacent hydrogeological structures treated separately so far revealed an experimentally confirmed hydraulic connection. An in-depth analysis of the problem showed the necessity of modifying the existing model of the structure in order to map the observed interactions. An additional simulation module of General-Head Boundary type was applied. The quantity of lateral groundwater exchange between two hydrogeological structures was estimated using mathematical modeling at 3.4 thousand m3/d (reconstructed current state, after model calibration). Further work should aim at treating reservoirs as hydraulically connected after exceeding limiting parameters.

This paper deals with the numerical solution of space-time fractional partial differential-difference Toda lattice equation $\frac{\partial^{2\alpha} u_n}{\partial x^{\alpha}\partial t^{\alpha}}=(1+\frac{\partial^\alpha u_n}{\partial t^{\alpha}})(u_{n-1}-2u_n+u_{n+1})$, $\alpha \in (0,1)$. The finite differences method (FD-method) is used for numerical solution of this problem. According to the method, we approximate the unknown values $u_n$ of the desired function by finite differences approximation. As an application we demonstrate the capabilities of this method for identification of various values of order of fractional derivative $\alpha$. Numerical results show that the proposed version of FD-method allows to obtain all data from the initial and boundary conditions with enough high accuracy.

In this study, the singular boundary method is applied to solve time-dependent pseudo-parabolic equations in two space dimensions with initial and Dirichlet-type boundary conditions. A splitting procedure is used to split the solution of the inhomogeneous governing equation into a homogeneous solution and a particular solution. This work presents the numerical operation for calculating the particular solution and homogeneous solution. Several numerical examples are provided to show the accuracy and efficiency of the method. Furthermore, the analysis of stability and convergence is presented. [ABSTRACT FROM AUTHOR]

In this paper, a new approach for interpreting raw pulsed electroacoustic (PEA) signals is proposed. The theory behind acoustic wave propagation in ideal (no attenuation and no dispersion) materials and in real materials (with attenuation and dispersion) initially free of space charge is described. A simulation model has been developed for the following: (1) the acoustic signal formation in the PEA apparatus, the transmission of the acoustic waves, their attenuation/dispersion and detection; (2) the instrumental effects of having a capacitive piezoelectric sensor driving a 50 Ω input impedance amplifier. The various layers of a PEA system were considered in the model and the effect of each layer on the acoustic wave propagation is analyzed. Since the model allowed raw PEA data to be simulated, it can be used to identify potential sources of error in interpreting real PEA measurement data, such as acoustic mismatch between PEA layers, electrode material effects, pulse voltage, etc. The results showed good agreement between the simulated and experimentally obtained data in the case of space charge free samples. [ABSTRACT FROM AUTHOR]

In this paper, we have numerically studied the phenomenon of unidimensional convectionconduction equation in a channel, cylinder and sphere immersed in a solar pond. Then we have studied bidimensional case in a heat exchanger, which undergoes an external heat flow provided by solar pond. We carried out the discretization of the mathematical model by finite differences method (explicit scheme). Calculation codes in Fortran language have been created for the temperature distribution in all these geometries. We presented the numerical results in terms of temperature profile functions, one- and two-dimensional, in laminar flow regime, for various parameters. We also present a study by COMSOL of the same phenomenon on these geometries. This study can be presented by two methods, the first using the physical model and the second using the mathematical part of COMSOL. [ABSTRACT FROM AUTHOR]

The temperature of annealed steel coils is a determining variable of the future steel sheets quality. This variable also determines the energy consumption in operation. Unfortunately, the monitoring of coil inner temperature is problematic due to the furnace environment with high temperature, coil structure, and annealing principle. Currently, there are no measuring principles that can measure the temperature inside the heat-treated product in a non-destructive manner. In this paper, the soft sensing of inner temperature based on the theory of non-stationary heat conduction and approach based on Support Vector Regression (SVR) was presented. The results showed that a black-box approach based on the SVR could replace an analytic approach, though with lesser performance. Several annealing experiments were performed to create a training data set and model performance improvement in the estimation of inner coil temperatures. The proposed software based on non-stationary heat conduction can calculate the behavior of inner coil temperature from the measured boundary temperatures that are measured by thermocouples. The soft-sensing principles presented in this paper were verified under laboratory conditions and on the data obtained from a real annealing plant. [ABSTRACT FROM AUTHOR]

The buckling and post-buckling behavior of initially imperfect, sinusoidally curved hinged-hinged beams undergoing very large deflections subjected to lateral concentrated loads acting at the midpoints is investigated via the geometrically nonlinear analysis of the problem. The transverse shear deformation is neglected. The amplitudes of the imperfection are considered to be relatively small. Therefore, the concerning curved beams (or arches) are shallow. The values of the extensional rigidity/length of the beams are assumed to be large enough not to permit considerable amount of change in the lengths of the beams during the deformation. The force-deflection curves corresponding to various amplitudes of the imperfection and the diagrams of the deflections and internal forces corresponding to various stages of the deformation, including those after the buckling, are presented. Not being able to solve the highly nonlinear problem analytically, numerical methods are used. [ABSTRACT FROM AUTHOR]

This study proposes a method for forecasting commodities prices using Schwartz partial differential equation (PDE) and Kalman filtering. The method is applicable to both the single-factor and the multi-factor Schwartz PDE. Using semi-discretisation and the finite differences method, the Schwartz PDE is transformed into an equivalent state-space description. This latter representation is finally written in a linear matrix form in which the Kalman filter's recursion is applicable. By redesigning the Kalman filter as a m-step ahead predictor it becomes possible to obtain accurate estimates of the future commodities’ price. The prediction scheme analysed in this study can contribute to maximising profits in commodities trading, including also the trading of electric power.

The structural engineering researches have attracted considerable attention by many scientist for several decades. Determining the dynamical behaviors of structural elements with some discontinuous is of great importance in many engineering applications. The mentioned structures can be modelled two different ways. In the first approximation so-called the classical approach, a fourth order differential equation are written for each part of beam separated in the distinct discontinuity locations. Therefore, we obtain a system of equation containing n + 1 number of the differential equation with boundary and transient conditions. Secondly, the real problem can be reformulated by only one differential equation having discontinuity function. In this study, we introduce the method of multiple scales as the solution technique. Since we encountered by the differential equation with discontinuity function in the part of order discretization during the perturbative solution, we have used a numerical technique for the solution. The mentioned technique is applied on the beam model lying on lineer spring foundation called as Winkler type foundation. [ABSTRACT FROM AUTHOR]

In this paper, by using the fuzzy CESTAC method and the CADNA library a procedure is proposed to control the step size for solving the fuzzy differential equation with fuzzy boundary conditions based on the finite differences method under generalized H-differentiability (gH-differentiability). An algorithm is presented to implement the discrete stochastic arithmetic for solving the given fuzzy boundary value problem on the C++ code via the CADNA library. Also, a theorem is proved to show the accuracy of results based on the concept of the common proximity of two fuzzy numbers. Finally, some examples are solved by using the proposed algorithm to illustrate the effectiveness of applying the stochastic arithmetic (SA) in place of the floating-point arithmetic (FPA) to validate the results and find the optimal solution. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the pricing problem of a European-style contingent claim under a Markov-modulated exponential Lévy model. One of the main feature of this model is the modulator factor which takes into account the empirical facts observed in asset prices dynamics such as the long-term (stochastic) variability and time inhomogeneities. Using the viscosity solutions framework, we show that the value of a European-style option is the unique viscosity solution of a system of coupled linear Partial Integro-Differential Equations when the payoff function satisfies a Lipschitz condition. Moreover, we propose a numerical scheme for approximating solution of this system and discuss its stability, consistency and convergence. [ABSTRACT FROM AUTHOR]

We present a semi-numerical solution to a fractal telegraphic dual-porosity fluid flow model. It combines Laplace transform and finite difference schemes. The Laplace transform handles the time variable whereas the finite difference method deals with the spatial coordinate. This semi-numerical scheme is not restricted by space discretization and allows the computation of a solution at any time without compromising numerical stability or the mass conservation principle. Our formulation results in a non-analytically-solvable second-order differential equation whose spatial discretization yields a tridiagonal linear algebraic system. Moreover, we describe comparisons between semi-numerical and semi-analytical solutions for particular cases. Results agree well with those from semi-analytic solutions. Furthermore, we expose a parametric analysis from the coupled model in order to show the effects of relevant parameters on pressure profiles and flow rates for the case where neither analytic nor semi-analytic solutions are available. [ABSTRACT FROM AUTHOR]

Phenol formaldehyde resin (PFR) based composites with multiwalled carbon nanotube (MWCNT) additives (2 and 5 wt.%) were prepared and their electromagnetic (EM) properties were investigated in Ka‐band frequency range (26–37 GHz). It was demonstrated that the combination of such materials in a double‐layered structure allows achievement of the significant attenuation of EM radiation. The electromagnetic response of considered double‐layered system was modeled by solving the electric field integral equation, utilizing the Green's function technique. Absorption up to 96% in the 26–37 GHz frequency band was both predicted and experimentally observed. [ABSTRACT FROM AUTHOR]

This paper concerns the use of a point-value multiresolution algorithm and its extension to three-dimensional hyperbolic conservation laws. The proposed method is applied to a high-order finite-differences discretization with an explicit time integration. The fluxes are evaluated on the adaptive grid using a fifth-order high-resolution shock capturing scheme based on a WENO solver, while the time is advanced using a third-order Runge–Kutta scheme. The multiresolution prediction operators are presented for one-, two- and three-dimensional problems. To assess the efficiency and the accuracy of the method, a new tolerance-scale diagram is introduced. This diagram enables to properly choose the adequate value of the tolerance in order to maintain an optimal multiresolution quality. Numerical examples based on advection and Euler equations are carried out to show that the proposed method yields accurate results. [ABSTRACT FROM AUTHOR]

In this work, we present a methodological procedure to validate the numerical solution of the diffusive part in a reaction–diffusion model. Uniform explicit finite differences method is used to generate the solution in a confined circular domain with boundary condition of zero flux. For the validation of the numerical solution, we consider three different criteria applied to normal diffusion and sub-diffusive cases: (i) the moments of concentration, ​(ii) decay of the concentration at the origin and (iii) the mass conservation. The numerical solution fulfills the validation criteria of moments and concentration decay at the origin only in the long-term. The mass conservation criterion is fulfilled when the initial condition is imposed close to the border, whereas when it is set near to the origin a dependence on the diffusion rate appears. Pattern formation is presented after validating the numerical solution for normal diffusive case. Good agreement of stationary spatial pattern against reported results is observed. [ABSTRACT FROM AUTHOR]

In this article, we study a spectral meshless radial point interpolation of pseudoparabolic equations in two spatial dimensions. Shape functions, which are constructed through point interpolation method using the radial basis functions, help us to treat problem locally with the aim of high-order convergence rate. The time derivatives are approximated by the finite difference time-stepping method. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical results are presented to illustrate the theoretical findings. © 2016 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 724-741, 2017 [ABSTRACT FROM AUTHOR]

This work is a contribution to a better understanding of the effect that domestic sewage discharges may cause in a water body, specifically at Igapó I Lake, in Londrina, Paraná State, Brazil. The simulation of the dynamics of pollutant concentrations throughout the water body was conducted by means of structured discretization of the geometry of Igapó I Lake, together with the finite differences and the finite elements methods. Firstly, the hydrodynamic flow (without the pollutants), modeled by Navier-Stokes and pressure equations, was numerically resolved by the finite differences method, and associated with the fourth order Runge-Kutta procedure. After that, by using the hydrodynamic field velocity, the flow of the reactive species (pollutants) was described through a reaction transport model, restricted to the carbon-nitrogen cycle. The reaction transport model was numerically resolved by the stabilized finite elements method, by means of a semi-discrete formulation. A qualitative analysis of the numerical simulations provided a better understanding of the dynamics of the processes involved in the flow of the reactive species, such as the dynamics of the nitrification process, of the biochemical demand of oxygen and of the level of oxygen dissolved in the water body at Igapó I Lake.

In order to reduce the heat and mass transfers in buildings, which increase energy bills, the development of composites materials such as earth bricks stabilized with thatch fibers is important for their construction. This paper aims to study a one-dimensional model of heat and moisture transfer through porous building materials. The coupled phenomena of heat and mass transfer are described by the Luikov model. Equations and boundary conditions are discretized using the finite difference method. The results obtained illustrate the temporal evolutions of the temperature and the moisture content, as well as the distributions of the temperature and moisture content inside the wall. The profile of the temperature and water content that are obtained are compared with the other numerical solutions that are available in the literature.

Comparison between hydraulic and hydrologic computational methods is conducted in this study, regarding prismatic open channels under unsteady subcritical flow conditions. One-dimensional unsteady flow continuity and momentum equations are solved using explicit and implicit finite difference schemes for a symmetrical trapezoidal cross section, where the flow discharge and depth are the dependent variables. The results have been compared to those derived from Muskingum-Cunge hydraulic/hydrologic method as well as the commercial software HEC-RAS. The results from explicit and implicit code compare well to those from commercial software and hydraulic/hydrologic methods for long prismatic channels, thus directing the hydraulic engineer to quick preliminary design of prismatic open channels for unsteady flow with satisfactory accuracy.

Deflection of foundation girder supported by the deformable base has been defined by the system of differential equations, where the differential equation of the elastic line of the girder is of the fourth order. The most convenient solution of the problem is application of numerical procedures, in this case it is the finite difference method. In the paper, the mentioned method is applied in the special case of foundation girder of variable cross section loaded by arbitrary load on its ends.

In this investigation, steady two – dimensional natural convection heattransfer of Newtonian and non-Newtonian fluids inside square enclosure has beenanalyzed numerically for a wide range of the modified Rayleigh number of (103 ≤Ra ≤ 105), with non-dimensional parameter(NE) of Prandtl – Eyring model rangingfrom (0 to 10), and modified Prandtl number in the range (Pr* =1,10, and 100).Two types of boundary conditions have been considered. The first,is when the sidewalls are heated at different uniform temperatures and the horizontal walls areinsulated. The second, when the bottom wall is heated by applying a uniform heatflux while the other walls are at the constant cold temperature. Also, the non-Newtonian fluids under consideration were assumed to obey the Prandtl – Eyringmodel. The numerical results of the values of average Nusselt number have beenconfirmed by comparing them to similar known yeslts of previous works using thesame boundary conditions. Good agreement was obtained. The results arepresented in terms of isotherms and streamlines to show the behavior of the fluidflow and temperature fields. In addition, some graphics represent the relationbetween average Nusselt number and the parameters that are mentionedpreviously. The results show the effect of non – dimensional parameter (NE) on thevelocity and temperature profiles. It also shows that the average Nusselt number isa strong function of modified Rayleigh number, modified Prandtl number, nondimensionalparameter, and the boundary conditions. Four different correlationshave been made to show the dependence of the average Nusselt number on thenon-dimensional parameter, the modified Rayleigh and Prandtl numbers.

Elliptic partial differential equations (ePDEs) appear in a wide variety of areas of mathematics, physics and engineering. Typically, ePDEs must be solved numerically, which sets an ever growing demand for efficient and highly parallel algorithms to tackle their computational solution. The Scheduled Relaxation Jacobi (SRJ) is a promising class of methods, atypical for combining simplicity and efficiency, that has been recently introduced for solving linear Poisson-like ePDEs. The SRJ methodology relies on computing the appropriate parameters of a multilevel approach with the goal of minimizing the number of iterations needed to cut down the residuals below specified tolerances. The efficiency in the reduction of the residual increases with the number of levels employed in the algorithm. Applying the original methodology to compute the algorithm parameters with more than 5 levels notably hinders obtaining optimal SRJ schemes, as the mixed (non-linear) algebraic-differential system of equations from which they result becomes notably stiff. Here we present a new methodology for obtaining the parameters of SRJ schemes that overcomes the limitations of the original algorithm and provide parameters for SRJ schemes with up to 15 levels and resolutions of up to 2 15 points per dimension, allowing for acceleration factors larger than several hundreds with respect to the Jacobi method for typical resolutions and, in some high resolution cases, close to 1000. Most of the success in finding SRJ optimal schemes with more than 10 levels is based on an analytic reduction of the complexity of the previously mentioned system of equations. Furthermore, we extend the original algorithm to apply it to certain systems of non-linear ePDEs. [ABSTRACT FROM AUTHOR]

In this paper, the direct and inverse initial boundary value problems for a first order system of two hyperbolic equations are considered. The method of characteristics and the finite difference method are applied to the theoretical and numerical solutions of the direct problem, respectively. Moreover the suitability of the method of characteristics for the inverse problem of finding solely space-dependent coefficients and the finite difference method for solely time-dependent coefficients of the first order hyperbolic system are shown. The stability of the numerical method is supported by the examples. [ABSTRACT FROM AUTHOR]

Integral and differential equations have a fundamental importance in the functional analysis and the practice problems, and many domains of scientific research. However, the resolution of differential equations with constant coefficients is easy, but the resolution of these equations with variable coefficients is practically difficult or impossible in more part of the cases. This work present a analytical method which it transform a differential equations with initial conditions to a Volterra equations of second kind, efficient methods for approximate numerical solution of these equations, the analysis of the existence of their solutions, and the convergence of the error. [ABSTRACT FROM AUTHOR]

• Thermal conductivity measurements on timber materials at different temperatures and moisture contents. • Heat and mass transfer modelling for different timber buildings' components in Italian climates. • Assessment of the impact of temperature and moisture content on the heat flux across timber components. Even if many studies in the literature confirm that the thermal properties of several building materials are highly affected by the material's temperature and moisture content, it is common practice in building performance simulation to adopt constant properties, such as thermal conductivity. Those values are usually estimated according to the technical standard EN 10456:2007. This modelling choice can introduce inaccuracies in the calculation of the heat and mass transfer across the opaque building envelope, especially for some types of buildings such as the timber ones. With the goal of assessing and quantifying the extent of these inaccuracies in timber components, this research combined experimental and numerical analyses. First, dynamic thermal conductivity functions dependent on temperature and moisture content were determined for some typical timber materials (cross-laminated timber, woodchips, and wood-fibre panels). Then, annual hourly simulations were run for a set of different timber components in a Mediterranean and an Alpine Italian climate, considering four different approaches of increasing complexity and level of detail for the determination of the thermal conductivity values. Results reveal that the current standard approach based on the constant thermal conductivity determined in agreement with the EN 10456:2007 conditions can lead to significant inaccuracies compared to more detailed alternatives, whose values can be affected by the climate, the component's position, and orientation, as well as its solar absorptance. The heat flux across a horizontal roof placed in a warm and humid Mediterranean climate can increase up to a +9 % when considering a dynamic thermal conductivity instead of the constant approach. [ABSTRACT FROM AUTHOR]