A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement ...
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A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement algorithms of previous developed node potential analysis algorithm are presented. These enhancement algorithms are used for a reasonable setting of initial values in the numerical gas net simulation algorithm. The setting of the initial values has a significant influence on the convergence behavior of the numerical simulation. The presented enhancement algorithms are explained and simulation results are evaluated. Copyright (C) 2020 The Authors.
A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement ...
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A reliable energy supply for the economy of every country is a matter of national importance. Powerful simulation tools for natural gas networks are essential for operators of gas networks. In this paper, enhancement algorithms of previous developed node potential analysis algorithm are presented. These enhancement algorithms are used for a reasonable setting of initial values in the numerical gas net simulation algorithm. The setting of the initial values has a significant influence on the convergence behavior of the numerical simulation. The presented enhancement algorithms are explained and simulation results are evaluated.
In this paper, we present a computational method for solving the second-order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The ...
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In this paper, we present a computational method for solving the second-order impulsive differential equations with loadings subject to integral boundary conditions based on the Dzhumabaev parametrization method. The idea of this method involves introducing additional parameters, reducing the original problem to solving a system of linear algebraic equations. The system's coefficients and right-hand side are determined by solving Cauchy problems for ODEs and by calculating definite integrals. Four examples are provided to show the effectiveness and feasibility of the main results.
The non-Newtonian (NN) Prandtl-Eyring fluid (PEF) model can be used to optimize conditions for processing, ensure substance high quality and consistency, and anticipate melted polymer flow behavior. This paper looks i...
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The non-Newtonian (NN) Prandtl-Eyring fluid (PEF) model can be used to optimize conditions for processing, ensure substance high quality and consistency, and anticipate melted polymer flow behavior. This paper looks into an intriguing feature of irreversibility estimation through NN-PEF flow over a curved Riga surface. The impact of second-order slip conditions, thermal radiation, and exponential heat source/sink are also elaborated. The flow equations of NN-PEF have been reformulated into a dimensionless representation of differential equations (DEs) with an application of similarity conversions. The obtained lowest-order differential equations are numerically solved through the PCM (parametric continuation method). For accuracy of the results, the outcomes are compared to both experimental and theoretical results. The relative percent error between the present findings and the published numerical results at Re = 5000 is 0.71094 %. The rate of heat transfer (W/ m2K) enhances from 4238.0724 to 44390.4205 at Re = 1594 to 440. The relative error between published experimental and present results is about 0.0029 % at Re = 440, which ensures the reliability of the proposed model and applied methodology. The velocity field of PEF is significantly boosted with the positive variation in 1st and 2nd order slip parameters. The influence of the Brinkmann number and heat radiation factor is enhanced, while the consequences of the temperature ratio parameter drop the rate of entropy generation in the system.
This paper establishes a general computational framework to solve the muti-scale contact problem by integrating the statistical contact model with the finite element format. Compared to existing models, the proposed m...
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This paper establishes a general computational framework to solve the muti-scale contact problem by integrating the statistical contact model with the finite element format. Compared to existing models, the proposed method is applicable to most geometric configurations and can effectively evaluate the pressure distribution. In this work, a modified Karush-Kuhn-Tucker (KKT) condition is proposed by the assumption that asperity height obeys the Gaussian distribution. Therefore, in the variational formula, the contact contribution is decomposed into body contribution and asperity contribution, corresponding to the nominal smooth surface and roughness, respectively. Then the linearization and constraint enforcement of these two components are derived, followed by a nonlinear Newton-Raphson-based iterative algorithm. The contact patch test and Hertz contact test are conducted, and the predicted results are consistent with the theoretical and experimental values, confirming the effectiveness and accuracy of the proposed approach. It is worth noting that in the Hertz contact test, the contact pressure distribution varies progressively with the roughness level and external force, tending to the Hertz limit or Gaussian limit. This means that the proposed method can be applied to any roughness and load. Finally, the contact behaviors of the transmission interface of a piezoelectric actuator, i.e., a typical multi-scale contact problem, are studied as an engineering application case.
In certain pressure and temperature ranges, high-precision thermal equations of state possess multiple roots, with only one being the desired physical solution to the problem. This paper considers methods for setting ...
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In certain pressure and temperature ranges, high-precision thermal equations of state possess multiple roots, with only one being the desired physical solution to the problem. This paper considers methods for setting initial values to calculate the desired root of the equation. A method for verifying the found root has been developed, enabling the exclusion of nonphysical solutions. The proposed approach allows for the construction of a robust algorithm for numerically solving transcendental equations of state for practical applications.
In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to ...
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In this paper, we consider the numerical solutions of three-dimensional axisymmetric nonlinear boundary integral equations with logarithmic kernel. A numerical algorithm with using extrapolation twice is developed to solve the equations, which possesses the low computing complexities and high accuracy. The asymptotic compact operator theory is used to prove the convergence of the algorithm. The efficiency of the algorithm is illustrated by numerical examples.
To facilitate images under the nonlinear geometric transformation T and its inverse transformation T-1, we have developed numerical algorithms in [1]-[19]. A cycle conversion T-1T of image transformations is said if a...
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To facilitate images under the nonlinear geometric transformation T and its inverse transformation T-1, we have developed numerical algorithms in [1]-[19]. A cycle conversion T-1T of image transformations is said if an image is distorted by a transformation T and then restored back to itself. The combination (CSIM) of splitting-shooting-integrating methods was first proposed in Li [1] for T-1T. In this paper other two combinations, CUM and C&IM, of splitting integrating methods for T-1T are provided. Combination CSIM has been successfully applied to many topics in image processing and pattern recognition (see [2]). Since combination CSIM causes large greyness errors, it well suited to a few greyness level images, but needs a huge computation work for 256 greyness level images of enlarged transformations (see [16]). We may instead choose combination CIIM which involves nonlinear solutions. However, the improved combination CI#IM may bypass the nonlinear solutions completely. Hence, both CIIM and CI#IM can be applied to q(q greater than or equal to 256) greyness level images of arty enlarged transformations. On the other hand, the combined algorithms, CSIM, CIIM, and CI#IM, are applied to several important topics of image processing and pattern recognition: binary images, multi-greyness level images, image condensing, illumination, affine transformations, prospective and projection, wrapping images, handwriting characters, image concealment, the transformations with arbitrary shapes, and face transformation. This paper may also be regarded as a review of our recent research papers [1]-[19].
作者：
Peng, ShigeXu, MingyuShandong Univ
Sch Math & Syst Sci Jinan 250100 Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Key Lab Random Complex Struct & Data Sci Beijing Peoples R China Fudan Univ
Sch Math Sci Dept Financial Math & Control Sci Shanghai 200433 Peoples R China
In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE...
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In this paper we study different algorithms for backward stochastic differential equations (BSDE in short) basing on random walk framework for 1-dimensional Brownian motion. Implicit and explicit schemes for both BSDE and reflected BSDE are introduced. Then we prove the convergence of different algorithms and present simulation results for different types of BSDEs.
In this paper, a new approach to the disease transmission dynamics of the COVID-19 pandemic is presented, involving the use of game theory and dual dynamic programming. A new compartmental model that describes these d...
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In this paper, a new approach to the disease transmission dynamics of the COVID-19 pandemic is presented, involving the use of game theory and dual dynamic programming. A new compartmental model that describes these dynamics is introduced. New classes have been added to this model to account for the portion of the population vaccinated with one dose, two doses, or three doses. Pandemic costs are also included. Time-dependent parameters (strategies) are employed, allowing for the consideration of different behavior variants and decisions made by policymakers. Sufficient conditions for a dual epsilon-closed-loop Nash equilibrium, are formulated in the form of a verification theorem. A numerical algorithm is constructed, and numerical simulations are performed. A comparison between real pandemic data for Poland and the data obtained from the model is made.
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