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Analysis of the slipstream development around the high-speed trains in tunnels would provide references for assessing the transient gust loads on trackside workers and trackside furniture in tunnels. This paper focuses on the computational analysis of the slipstream caused by high-speed trains passing through double-track tunnels with a cross-sectional area of 100 m2. Three-dimensional unsteady compressible Reynolds-averaged Navier-Stokes equations and a realizable k-ε turbulence model were used to describe the airflow characteristics around a high-speed train in the tunnel. The moving boundary problem was treated using the sliding mesh technology. Three cases were simulated in this paper, including two tunnel lengths and two different configurations of the train. The train speed in these three cases was 250 km/h. The accuracy of the numerical method was validated by the experimental data from full-scale tests, and reasonable consistency was obtained. The results show that the flow field around the high-speed trains can be divided into three distinct regions: the region in front of the train nose, the annular region and the wake region. The slipstream development along the two sides of train is not in balance and offsets to the narrow side in the double-track tunnels. Due to the piston effect, the slipstream has a larger peak value in the tunnel than in open air. The tunnel length, train length and length ratio affect the slipstream velocities; in particular, the velocities increase with longer trains. Moreover, the propagation of pressure waves also induces the slipstream fluctuations: substantial velocity fluctuations mainly occur in front of the train, and weaken with the decrease in amplitude of the pressure wave. [ABSTRACT FROM AUTHOR]

In this paper, the authors study the forward and inverse problems for a fractional boundary value problem with Dirichlet boundary conditions. The existence and uniqueness of solutions for the forward problem is first proved. Then an inverse source problem is considered. [ABSTRACT FROM AUTHOR]

In the present study, numerical simulations of two-dimensional steady-state incompressible Newtonian fluid flow in one-sided square and two-sided deep lid driven cavities under the aspect ratio K = 1, 4, 6 are reported. For the one-sided lid driven cavity, the upper wall is moved to the right with up to 5000 Reynolds numbers under a grid size of up to 501 × 501. This lends support to previous findings in the literature with Ghia et al.’s results. Three cases are used in this article for the two-sided deep lid driven square cavity specifically. In these cases, the top and lower walls are moved to the right, while the left and right walls remain fixed up to at high Reynolds numbers (5000) under the grid size of up to 201×201. All possible flow solutions are studied in the present article, and flow bifurcation diagrams are constructed as velocity profiles and streamline contours for the same Reynolds number using a finite volume SIMPLE technique. The work done in this paper includes flow properties such as the location of primary and secondary vortices, velocity components, and numerical values for benchmarking purposes, and it is in excellent agreement with previous findings in the literature. A PARAM Shavak, high-performance computing (HPC) computer, was used to execute the calculations. [ABSTRACT FROM AUTHOR]

In this paper, we study a one-dimensional morphogenesis model considered by C. Stinner et al. (Math. Meth. Appl. Sci. 2012; 35: 445-465). Under homogeneous boundary conditions, we prove the existence of nonconstant positive steady states through local bifurcation theories. Then we rigorously study the stability of these nonconstant solutions when the sensitivity functions are chosen to be linear and logarithmic, respectively. Finally, we present numerical solutions to illustrate the formation of stable inhomogeneous spatial patterns. Our numerical simulations show that this model can develop very complicated and interesting structures even over one-dimensional finite domains. [ABSTRACT FROM AUTHOR]

In this paper, we explore how the behavior of cellular automata (CAs) is affected by different boundary conditions and what types of systems it is affected by. Six experiments are presented. The first determines the most effective boundary condition for optimizing rule-output (in)equality related to Shannon entropy. The second experiment determines the effect of the boundary conditions compared to the size of the initial conditions. The third experiment determines the variation of systems for a specific Li-Packard and Wolfram class. The fourth experiment generalizes the principles of the third experiment into a rule space involving four binary cells rather than three. The fifth experiment determines the change in complexity of systems with different boundary conditions. Finally, the sixth experiment generalizes the concepts of the fifth experiment into the same rule space used in experiment four. Most of the time, boundary conditions do not change the classification, thus do not change the behavior. But some boundary conditions have been found to change the qualitative behavior. However, it is only constant boundary conditions that have been found to change the complexity of a system, and the constant boundary conditions only decrease the complexity. The largest change in the compression ratio was found to be for rule 110 when the boundary conditions change from cyclical to constant. The degree of this change is approximately 25%. Distributed and cyclical boundary conditions can be relied upon to maximize the rule-output equality of systems in general, while null boundary conditions can be relied upon to increase the overall complexity of a system. [ABSTRACT FROM AUTHOR]

An ordinary differential equation (ODE) can be split into simpler sub equations and each of the sub equations is solved subsequently by a numerical method. Such a procedure involves splitting error and numerical error caused by the time stepping methods applied to sub equations. The aim of the paper is to present an integral formula for the global error expansion of a splitting procedure combined with any numerical ODE solver. [ABSTRACT FROM AUTHOR]

We perform simulations in a gravitational collapsing model using the Einstein equations. In this paper, we review the equations for constructing the initial values and the evolution form of the Einstein equations called the BSSN formulation. In addition, since we treat a nonvacuum case, we review the evolution equations of the matter fields of a perfect uid. To make the simulations stable, we propose a modified system, which decreases numerical errors in analysis, and we actually perform stable simulations with decreased numerical errors. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analytical study of initial–boundary value problems for a system of hyperbolic balance laws derived from a repulsive chemotaxis model with logarithmic sensitivity. In the first part of the paper we show that, subject to the Dirichlet boundary conditions, classical solutions exist globally in time for large initial data. Asymptotically in time, the solutions are shown to converge to their boundary data at an exponential rate as time goes to infinity. Numerical simulations are supplied to corroborate the analytical results. The analytic approach developed herein can be utilized to handle a family of initial and initial–boundary value problems of the model and related models with similar mathematical structure. As a demonstration of the effectiveness of our approach, in the second part of the paper we show that, subject to the Neumann–Dirichlet boundary conditions, classical solutions exist and converge to constant equilibrium states for large initial data and for arbitrary values of the chemical diffusion coefficient. This improves a previous result obtained in [30] where the smallness of the chemical diffusion coefficient was required. [ABSTRACT FROM AUTHOR]

Two systems of Earth-centered inertial Newtonian orbital equations for a spherical Earth and three systems of post-Newtonian nonlinear equations, derived from the second post-Newtonian approximation to the Earth Schwarzschild field, are used to carry out a performance analysis of a numerical procedure based on the Dormand-Prince method for initial value problems in ordinary differential equations. This procedure provides preliminary post-Newtonian corrections to the Newtonian trajectories of middle-size space objects with respect to space-based acquisition, pointing, and tracking laser systems, and it turns out to be highly efficient. In fact, we can show that running the standard adaptive ode45 MATLAB routine with the absolute and relative tolerance, TOLa = 10−16 and TOLr = 10−13, respectively, provides corrections that are final within the eclipses caused by the Earth and close to final during the noneclipse phases. These corrections should be taken into account to increase the pointing accuracy in implementing the space-to-space laser links required for ablation of designated objects or communications between space terminals. [ABSTRACT FROM AUTHOR]

In this paper, the appearing probability of truck is introduced and an extended car-following model is presented to analyze the traffic flow based on the consideration of driver's characteristics, under honk environment. The stability condition of this proposed model is obtained through linear stability analysis. In order to study the evolution properties of traffic wave near the critical point, the mKdV equation is derived by the reductive perturbation method. The results show that the traffic flow will become more disorder for the larger appearing probability of truck. Besides, the appearance of leading truck affects not only the stability of traffic flow, but also the effect of other aspects on traffic flow, such as: driver's reaction and honk effect. The effects of them on traffic flow are closely correlated with the appearing probability of truck. Finally, the numerical simulations under the periodic boundary condition are carried out to verify the proposed model. And they are consistent with the theoretical findings. [ABSTRACT FROM AUTHOR]

The paper presents the Finite Element formulation of the equations proposed by Tsiampousi et al. (2016) for coupled consolidation in unsaturated soils. Their coupling is discussed in relation to a conceptual model which divides soil behaviour into zones ranging from fully saturated to dry states. The numerical simulation of a laboratory experiment involving drainage of water from a vertical column of sand is used to validate the equations. Finally, the example of rainfall infiltration into a cut slope highlights how aspects of the conceptual model are reflected in the numerical analysis of boundary value problems involving unsaturated soils. [ABSTRACT FROM AUTHOR]

We present effective methods for the numerical simulation of high-power-pumped continuous-wave (CW) and pulsed erbium-ytterbium-codoped fiber amplifiers (EYDFAs). For CW EYDFAs, a novel initial guess method and a robust algorithm are proposed to ensure the convergence of the boundary-value problems involved in the solution of the numerical model. For pulsed EYDFAs, an efficient finite-difference method based on the Lax-Wendroff scheme is developed. With these methods, high-power CW or pulsed EYDFAs can be simulated. As an example, a high-power pulse-pumped low repetition rate EYDFA is analyzed. Besides demonstrating the proposed methods, the simulation results show that the optimal pulse width of the pump can be determined by the power of the backward Yb-ASE, and the time delay between the signal and pump pulses play an important role in optimizing the performance of a high power pulse-pumped EYDFA. [ABSTRACT FROM AUTHOR]

This paper is concerned with the observer design for one-dimensional linear parabolic partial differential equations whose output is a weighted spatial average of the state over the entire spatial domain. We focus on the backstepping approach, which provides a systematic procedure to design an observer gain for systems with boundary measurement. If the output is not a boundary value of the state, the backstepping approach is not directly applicable to obtaining an observer gain that stabilizes the error dynamics. Therefore, we attempt to convert the error system into another system to which backstepping is applicable. The conversion is successfully achieved for a class of weighting functions, and the resultant observer realizes exponential convergence of the estimation error with an arbitrary decay rate in terms of the L 2 norm. In addition, an explicit expression of the observer gain is available in a special case. The effectiveness of the proposed observer is also confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we will extend the lattice Boltzmann model (LBM) to deal with the complex coupled nonlinear Schrödinger equations. A D1Q5 nonstandard complex lattice Boltzmann model (CLBM) with amending term for the coupled nonlinear Schrödinger equations (CNLSEs) is proposed. Complex equilibrium distribution functions and amending terms are selected, and the CNLSEs can be recovered by using the Chapman–Enskog multi-scale analysis and Taylor expansion technique. Some initial boundary value problems of the coupled system are simulated to verify the effectiveness and stability of our model. [ABSTRACT FROM AUTHOR]

Inclined overflow gates are widely used in open channels to meet different flow rate requirements by promptly adjusting their openings according to varied water levels. The characteristics of such gates are quite complex and need intensive study. To develop an effective and efficient numerical method for studying the hydrodynamic features of similar engineering structures with fluid structure interactions and free-surface flows, we propose a free-surface lattice Boltzmann-immersed boundary (FSLB-IB) coupling model, in which the free-surface flow is modeled by the lattice Boltzmann (LB) method and the moving boundaries are handled by the immersed boundary (IB) method. To solve the incompatibility issue arising from the coupling of the FSLB model and IB method, two treatments, namely the velocity correction in the empty cells for matching the IB speed with the local fluid velocity, and the iterative force-correction for enhancing accuracy, are introduced. The feasibility and accuracy of the proposed coupling scheme are first validated by two benchmark cases. Then the FSLB-IB scheme is applied to analyze the hydraulic characteristics of an inclined overflow gate in different working conditions. The good agreements between the simulated and empirical hydraulic parameters as well as the reasonable flow features show that the proposed coupling scheme is feasible for simulating practical hydraulic problems. [ABSTRACT FROM AUTHOR]

This article is concerned with the efficient and accurate simulation and optimization of linear Timoshenko beam networks subjected to external loads. A solution scheme based on analytic ansatz-functions known to provide analytic solutions for the deformation and rotation of a single beam with given boundary data is extended to the full network. It is demonstrated that the analytic approach is equivalent to a finite element (FE) method where only one element with a suitably chosen shape function per beam is required. The solution of the FE-type system provides analytic solutions at the nodes, from which the solutions along the beams can be reconstructed. Consequently analytic solutions for the network can be computed by a numerical scheme without applying a spacial discretization. While the assembly of the local stiffness matrices is slightly more expensive compared to an FE model using, e.g., linear ansatz-functions, the complexity of the solution of the FE-system is not. This is particularly interesting for topology and material optimization problems formulated on the network. In order to demonstrate the efficiency of the approach a numerical comparison to the case of linear ansatz-functions is provided followed by a series of studies with topology and multi-material optimization problems on networks. [ABSTRACT FROM AUTHOR]

We present a local and point-wise scheme for imposing reflective boundary conditions to stationary internal boundaries for solving the reactive Euler equations on Cartesian grids. The scheme is presented in two and three dimensions and can run efficiently on parallel machines while still maintaining the same advantages over other methods for enforcing internal boundary conditions. Level sets are used to represent internal solid regions along with a new local node sorting algorithm that decouples internal boundary nodes by establishing their connectivity to other internal boundary nodes. This approach allows us to enforce boundary conditions via a direct procedure, removing the need to solve a coupled system of equations numerically. We examine the accuracy and fidelity of our internal boundary algorithm by simulating flows past various solid boundaries in two and three dimensions, showing good agreement between our numerical results and experimental data. [ABSTRACT FROM AUTHOR]

An efficient local extrapolation of the exponential operator splitting scheme is introduced to solve the multi-dimensional space-fractional nonlinear Schrödinger equations. Stability of the scheme is examined by investigating its amplification factor and by plotting the boundaries of the stability regions. Empirical convergence analysis and calculation of the local truncation error exhibit the second-order accuracy of the proposed scheme. The performance and reliability of the proposed scheme are tested by implementing it on two- and three-dimensional space-fractional nonlinear Schrödinger equations including the space-fractional Gross-Pitaevskii equation, which is used to model optical solitons in graded-index fibers. [ABSTRACT FROM AUTHOR]