Search

In this paper, a methodical approach is presented to approximate the multi-term fractional advection-diffusion model (MT-FAD). The Lagrange squared interpolation is used to discretize temporal fractional derivatives, and Legendre polynomials are shifted as an operator to discretize the spatial fractional derivatives. The advantage of these numerical techniques lies in the orthogonality of Legendre polynomials and its matrix operations. A quadratic implicit design as well as its stability and convergence analysis are evaluated. It should be noted that the theoretical proof obtained from this study represents the first results for these numerical schemes. Finally, we provide three numerical examples to verify the validity of the proposed methods and demonstrate their accuracy and effectiveness in comparison with previous studies shown in [W. P. Bu, X. T. Liu, Y. F. Tang, J. Y. Yang, Finite element multigrid method for multi-term time fractional advection diffusion equations, Int. J. Model. Simul. Sci. Comput., 6 (2015), 1540001].

In this paper, we present a well-organized method to estimate the one-dimensional fractional Rayleigh–Stokes model using the construction of orthogonal Gegenbauer polynomials (GBPs) and Lagrange square interpolation to estimate the time derivative. Therefore, we design an authentic and fast numerical calculation approach based on the elaborated convergence rate recovery method. The matrix of the derivative operation of an orthogonal GBP is gained by employing the characteristic of this type of polynomial. The privilege of the numerical method is the orthogonality of the GBP and operational matrices, which reduces time computation and increases speed. Eventually, we propose three numerical examples to check the validity and numerical studies to illustrate the precision and efficiency of the new approach.

In the present article‎, ‎to find the answer to the mobile-immobile advection-dispersion model of temporal fractional order $0< \beta \leq 1$ (MI-ADM-TF)‎, ‎which can be applied to model the solute forwarding in watershed catchment and flood‎, ‎the effective high-order numerical process is gonna be built‎.‎To do this‎, ‎the temporal-fractional derivative of the MI-ADM-TF is discretized by using the linear interpolation‎, ‎and the temporal-first derivative by applying the first-order precision of the finite-difference method‎. ‎On the other hand‎, ‎After obtaining a semi-discrete form‎, ‎to obtain the full-discrete technique‎, ‎the space derivative is approximated utilizing a collocation approach based on the Legendre basis‎.‎The convergence order of the implicit numerical design for MI-ADM-TF is discussed in that is linear‎.‎Moreover‎, ‎the temporal-discretized structure of stability is also discussed theoretically in general in the article‎.‎Eventually‎, ‎two models are offered to demonstrate the quality and authenticity of the established process‎.

Burger and Fisher diffusion transfer properties and reactions from the characteristics are studied using a non-linear equation. The nonlinear fractional Burgers–Fisher equation (NFB-FE) appears in realistic physical situations such as ultra-slow kinetics, Brownian motion of particles, anomalous diffusion, polymerases of ribonucleic acid and deoxyribonucleic acid, continuous random movement, and formation of wave patterns. The present study focuses on the collocation scheme based on the shifted Chebyshev basis (SCB) and the compact finite difference method to obtain the numerical scheme of the NFB-FE. The simulation model is created in the two steps: Initially, a semi-discrete is formed in a temporal sense, applying a linear approximation with an accuracy order of two. Next, we examine the unconditional stability and the convergence order. In the second stage, the collocation approach based on the SCB of the fourth type is used to discretize the spatial derivative parts and generate the full-discrete scheme.

In this paper, the space-time fractional advection-diffusion equation (STFADE) is considered in the finite domain that the time and space derivatives are the Caputo fractional derivative. At first, a quadratic interpolation with convergence order O(τ3-α) is applied to obtain the semi-discrete in time variable. Then, the Chebyshev collocation method of the fourth kind has been used to approximate the spatial fractional derivative. In addition, the energy method has been employed to show the unconditional stability and gained convergence order of the time-discrete scheme. Finally, the accuracy of the numerical method is analyzed and showed that our method is much more accurate than existing techniques.

The computation of the nonlinear fractional Burgers–Fisher problem stated in the Caputo sense is the topic of this paper. The model depicts the issue of biological invasion and can be found in a variety of fields, including ecology, physiology, and basic stage transition situations. To produce the time discretization, the suggested methodology employs a one-order correct expression in the first process. To generate the full-discretization in the second level, the spectral collocation method approach that relies on the Legendre basis is presented. The theoretical investigation confirms the temporal discretized formulation’s stability and convergence, which are examined in relation to the associated norm. Three test examples demonstrate the computing capability and efficiency of the approach. We can use the provided approach to resolve more engineering and physics models and can also increase the convergence order of the method.

Abstract Due to the importance of gas-phase chemical reaction kinetics in low-emission combustion, stirred tank reactors have been used for decades as an experimental tool to study high- and low-temperature oxidation. A Jet-Stirred Reactor (JSR) setup is valuable to determine the evolution of species mole fractions. For the accuracy of the experimental results, it is important that a JSR is designed such that the concentration field is as homogeneous as possible in order to avoid disturbance of the chemical kinetics. In this work, numerical simulations were performed to investigate the mixing in a JSR chamber. The turbulent structures inside the JSR and the nozzles are captured using Large Eddy Simulations. We conducted numerically a parametric study to evaluate the effects of thermodynamic conditions and geometrical parameters on the mixing characteristics. More specifically, the diameter of the spherical chamber is modified together with the diameter of the nozzles through which fresh gases are fed. The characterization of the gas flow inside a typical spherical JSR layout and results derived by the normalized standard deviation of a tracer mass fraction show that a reduction of the JSR diameter at high pressures improves the homogeneity. Further, we propose a new optimized configuration consisting of six nozzles pointing to the center of the reactor which provides a more uniform composition compared to the standard JSR design.

Due to the importance of the generalized nonlinear Klein-Gordon equation (NL-KGE) in describing the behavior of light waves and nonlinear optical materials, including phenomena such as optical switching by manipulating the dispersion and nonlinearity of optical fibers and stable solitons, we explain the approximation of this model by evaluating different classical and fractional terms in this paper. To estimate the fundamental function, we use a first-order finite difference approach in the temporal direction and a collocation method based on Gegenbauer polynomials (GP) in the spatial direction to solve the NL-KGE model. Moreover, the stability and convergence analysis is proved by examining the order of the new method in the time direction as O(dt). To demonstrate the efficiency of this design, we presented numerical examples and made comparisons with other methods in the literature. [ABSTRACT FROM AUTHOR]

In this simulation study, the flow and thermal characteristics of a novel rotary-piston engine, which is a kind of internal combustion engines, were investigated by computational fluid dynamics and the finite volume method. The structure of this engine is different to others, mainly for having 24 cylinders during the motoring mode. As a novel engine, creation of numerical models based on Reynolds average Navier Stokes (RANS) simulation and analysis of various speed engines on the flow and thermal fields during intake and compression strokes are the focus of this work. The results were illustrated in term of the streamline patterns, in-cylinder temperature and pressure profile, swirl ratio (SR), wall heat flux, and turbulent velocity fluctuation. The present study indicates that, the mean pressure, temperature trace, and heat loss from the wall increase when switching to a higher engine speed. The temperature distribution reveals that the maximum temperature is restricted in the center of the combustion chamber near top dead center (TDC). Also, the maximum amount of turbulent velocity and swirl ratio are achieved at the beginning of the intake stroke and near TDC. It is observed that the obtained numerical results are in general agreement with the available experimental data.

Background and Objectives: Interferon-gamma is an important cytokine, which facilitates immunity against intracellular pathogens. Several factors, including genetic variations of cytokine-producing genes have been shown to influence the progression and severity of Hepatitis C virus (HCV) infection. Methods: Between January and December 2012, 87 HCV-infected individuals and 89 individuals without HCV infection were recruited for the study of Single Nucleotide Polymorphism (SNP) at Interferon Gamma (IFNG) +874 T/A. After extraction of genomic DNA from Peripheral Blood Mononuclear Cells (PBMCs) in blood sample of the individuals, Amplification Refractory Mutation System (ARMS) polymerase chain reaction was performed to evaluate the SNP at this position. Results: The frequency of genotype TA was 62.1% in the HCV-infected group, while it was 47.2% for the control group (p=0.033). However, after adjusting for confounders (including alcohol consumption, drug addiction, transfusion, and tattoos), the genotypes at this position did not show any statistically significant association with HCV infection (adjusted P values were above 0.05). The frequency of allele A was slightly higher in patients than the controls (55.2% versus 48.3%).Carriers of A allele were more frequent in patients with HCV infection compared to the control group (55.17% in patients versus 48.31% in the control group; P=0.02). However, after adjustment for confounders, the results were no longer statistically significant (P=0.2). Conclusion: A carrier status for certain alleles and genotypes at Interferon Gamma (IFNG) +874 T/A may lead to higher susceptibility to HCV infection in a certain population.

The effect of upstream velocity perturbations on the response of a premixed flame was investigated in terms of the flame transfer function dependency on excitation frequency. In this study, the assumption of constant flame speed was extended and the effect of flame speed development was considered; i.e., the flame speed would grow with the time after ignition or with the distance from a flame-holder. In the present study, the kinematics of a conical flame was investigated by linearization of the front tracking equation of flame to uniform and convected fluctuations of the flow velocity and the response was compared with that of a V-shaped flame and the experimental data in the previous studies. The results show that the effect of flame speed development could influence a decreasing gain and increase the phase of the flame response to the uniform velocity oscillations in low and moderate frequencies. Comparing the variations in the gain of flame response upon normalized frequency, show that a conical flame has lower values than the V-flame. In other words, these flames might be less susceptible to combustion instabilities than the V-flames. Furthermore, the variations in phase of the V-flames responses, which show a quasi-linear behavior with normalized frequency, have higher values than the saturated behavior in phase of the conical flame responses. Also, considering that the flame speed development induces an increase in the gain and phase of the conical flame response to the convected velocity oscillations in certain frequencies; because the developed flame front has longer length in comparison to the flame front in constant flame speed model. Therefore, the flame length may be longer than convective wavelength and the heat release would be generated in different points of the flame; consequently the flow oscillations might exert a stronger impact on the unsteady heat release fluctuations.

In this paper, a methodical approach is presented to approximate the multi-term fractional advection-diffusion model (MT-FAD). The Lagrange squared interpolation is used to discretize temporal fractional derivatives, and Legendre polynomials are shifted as an operator to discretize the spatial fractional derivatives. The advantage of these numerical techniques lies in the orthogonality of Legendre polynomials and its matrix operations. A quadratic implicit design as well as its stability and convergence analysis are evaluated. It should be noted that the theoretical proof obtained from this study represents the first results for these numerical schemes. Finally, we provide three numerical examples to verify the validity of the proposed methods and demonstrate their accuracy and effectiveness in comparison with previous studies shown in [W. P. Bu, X. T. Liu, Y. F. Tang, J. Y. Yang, Finite element multigrid method for multi-term time fractional advection diffusion equations, Int. J. Model. Simul. Sci. Comput., 6 (2015), 1540001]. [ABSTRACT FROM AUTHOR]

In this paper, we present a well-organized strategy to estimate the fractional advectiondiffusion equations, which is an important class of equations that arises in many application fields. Thus, Lagrange square interpolation is applied in the discretization of the fractional temporal derivative, and the weighted and shifted Legendre polynomials as operators are exploited to discretize the spatial fractional derivatives of the space-fractional term in multi-term time fractional advection-diffusion model. The privilege of the numerical method is the orthogonality of Legendre polynomials and its operational matrices which reduces time computation and increases speed. A second-order implicit technique is given, and its stability and convergence are investigated. Finally, we propose three numerical examples to check the validity and numerical results to illustrate the precision and efficiency of the new approach. [ABSTRACT FROM AUTHOR]