Numerical simulation of sphere water entry problem using Eulerian–Lagrangian method

This paper looks at the hydrodynamic’s numerical simulation of a free-falling sphere impacting the free surface of water by using the coupled Eulerian–Lagrangian (CEL) formulation included in the commercial software ABAQUS. A 3D model of a sphere with an unsteady viscous transient flow condition is used for numerical simulation. The simulation is performed for sphere with different density. The simulation results are verified by showing the computed shape of the air cavity, displacement of sphere, pinch-off time and depth that agree well with experimental results.     

Large scale petroleum reservoir simulation and parallel preconditioning algorithms research

Solving large scale linear systems efficiently plays an important role in a petroleum reservoir simulator, and the key part is how to choose an effective parallel preconditioner. Properly choosing a good preconditioner has been beyond the pure algebraic field. An integrated preconditioner should include such components as physical background, characteristics of PDE mathematical model, nonlinear solving method, linear     

Finite element analysis of flood discharge atomization based on water–air two-phase flow

Flood discharge atomization is a phenomenon of water fog diffusion caused by the discharge of water from a spillway structure, which brings strong wind and heavy rainfall. These unnatural winds and rainfall are harmful for the safe operation of hydropower stations with high water heads. Compared to the method of prototype observations, physical models and mathematical models, which are semi-theoretical and semi-empirical, numerical simulation methods have the advantage of being not limited by a similar scale and are more economical. A finite element model is presented to simulate flood discharge atomization based on water–air two-phase flow in this paper. Equations governing flood discharge atomization are composed of partial differential equations of mass and momentum conservation laws with unknowns for pressure, velocity and the water concentration. The finite element method is used to solve the governing equations by adopting appropriate solution strategies to increase the convergence and numerical stability. Then, the finite element model is applied to a practical project, the Shuibuya hydropower station, which experienced a flood discharge in 2016. Simulation results show that the proposed model can simulate flood discharge atomization with efficient convergence and numerical stability in three dimensions, and good agreement was observed between numerical simulations and prototype observational data. Based on the simulation results, the mechanism of flood discharge atomization was analyzed.     

Li–Yorke sensitive and weak mixing dynamical systems

Akin and Kolyada in 2003 [E. Akin, S. Kolyada, Li–Yorke sensitivity, Nonlinearity 16 (2003), pp. 1421–1433] introduced the notion of Li–Yorke sensitivity. They proved that every weak mixing system (X, T), where X is a compact metric space and T a continuous map of X is Li–Yorke sensitive. An example of Li–Yorke sensitive system without weak mixing factors was given in [M. ?iklová, Li–Yorke sensitive minimal maps, Nonlinearity 19 (2006), pp. 517–529] (see also [M. ?iklová-Mlíchová, Li–Yorke sensitive minimal maps II, Nonlinearity 22 (2009), pp. 1569–1573]). In their paper, Akin and Kolyada conjectured that every minimal system with a weak mixing factor, is Li–Yorke sensitive. We provide arguments supporting this conjecture though the proof seems to be difficult.     

Forward mixing model in a rotating disc contactor for kerosene–acetic acid–water system

The application of an extraction column model which takes into account the influence of the forward mixing model is brought forward by generation of values of the mass transfer and axial dispersion coefficients required by the model. Values of these coefficients were generated from solute concentration profile measurements in a rotary disc contactor (RDC). The use of the Handlos–Baron drop mass transfer model was justified. The resulting continuous phase transfer coefficients were found to be dependent largely on disc speed. The accuracy of the forward mixing model for kerosene–acetic acid–water system was adequately presented and explained by the axial dispersion coefficient.     

Ergodic Type Problems and Large Time Behaviour of Unbounded Solutions of Hamilton–Jacobi Equations

We study the large time behavior of Lipschitz continuous, possibly unbounded, viscosity solutions of Hamilton–Jacobi Equations in the whole space ? ^N . The associated ergodic problem has Lipschitz continuous solutions if the analogue of the ergodic constant is larger than a minimal value λ_min. We obtain various large-time convergence and Liouville type theorems, some of them being of completely new type. We also provide examples showing that, in this unbounded framework, the ergodic behavior may fail, and that the asymptotic behavior may also be unstable with respect to the initial data.     

Large Sets and Overlarge Sets of Triangle-Decomposition

There are six types of triangles:undirected triangle,cyclic triangle,transitive triangle,mixed-1triangle,mixed-2 triangle and mixed-3 triangle.The triangle-decompositions for the six types of triangles havealready been solved.For the first three types of triangles,their large sets have already been solved,and theiroverlarge sets have been investigated.In this paper,we establish the spectrum of LT_i(v,λ),OLT_i(v)(i=1,2),and give the existence of LT_3(v,λ)and OLT_3(v,λ)with λ even.     

CFD simulation of deflagration–detonation processes using vector- and parallel computing systems

In this paper, we describe the state of computational fluid dynamics simulations (CFD) of deflagration and detonation processes in hydrogen–air mixtures, using vector- and parallel computing systems, which have been provided in the Institute for Safety Research and Reactor Technology (ISR) at the Forschungszentrum Jülich (FZJ). The R&D work is performed within the scope of an EC project on hydrogen safety that is addressed to the verification of models and criteria for the prediction of Deflagration-to-Detonation Transition (DDT) in hydrogen–air–steam systems under severe accident conditions. Particularly, we report on the present state and recent progress made in the establishment of the CRAY hardware cluster (T90, T3E, J90) with vector and parallel processing capabilities, as well as on the current achievement of the CFD software cluster (CFX, ERCO, DET, IFSAS), including test cases for verification and validation, with some illustrating examples. Emphasis is put on the multi-dimensional simulation of fast turbulent hydrogen flames, for instance, using the general purpose field code CFX from AEA. The numerical results are compared with experimental results, which have been obtained for various conditions in the Russian large scale RUT test facility. Specifically, we outline deflagration–detonation processes concerning the numerical resolution of reacting flows in complex geometries, applying mesh refinement or massively parallel processing. First test cases indicate that our modern field code cluster (MFCC) with high-performance supercomputer networking (HPCN) will be a suitable constellation to resolve DDT processes in safety enclosures of innovative nuclear reactor containments or other industrial plants, e.g. solar hydrogen demonstration facilities.     

Dynamic model of methane–water diffusion

This paper presents a mathematical model to describe the time evolution of the diffusion process of methane exchange between liquid and gaseous phases. In order to reach the equilibrium, the distribution of gas in the liquid phase decreases to a constant value over time. Generalized model is analyzed under the assumption that both, reversible and irreversible form of absorption and desorption, occur at the same time. For the application in case of the real system of methane–water, model is developed under the assumption that the processes of absorption and desorption are irreversible. From the experimental data are determined the coefficients of model and their dependence on initial conditions, with constant end conditions. This paper tests the introduced theoretical model on the existing experimental data.     

Numerical simulation of crack–propagation in shells

We develop a finite element method for the simulation of fragmentation of thin shells. The method is valid for completely non–linear problems, but is restricted to through–the–thickness cracks, which are normal to the midsurface. The methodology is based on the extended finite element method (X–FEM). The use of X–FEM allows arbitrary crack path evolution and does not require a priori knowledge of the crack zone or remeshing. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Multiscale analysis and simulation of a reaction–diffusion problem with transmission conditions

This paper considers a transmission problem for partial differential equations obtained in the recent paper [M. Neuss-Radu, W. Jäger, Effective transmission conditions for reaction-diffusion processes in domains separated by an interface, SIAM J. Math. Anal. 39 (2007) 687–720] as the effective system modeling a reaction–diffusion process in two domains separated by a membrane. For the analysis of this problem an appropriate function space, which includes the coupling conditions for the concentrations on the interface, is introduced. The transmission conditions for the flux are included in the variational formulation with respect to this function space.The solution of the transmission problem is approximated by using the Galerkin method. Numerically the problem is reduced to a system of ordinary differential equations, where the coupling of the micro- and macro-variables leads to a special structure, distinguishing the variables relevant for the transmission. Results of numerical simulations are illustrating the effect of the microscopic process in the membrane on the macroscopic reaction–diffusion process in the bulk domains.     

A comparison of one-dimensional and three-dimensional models for the simulation of gas–solids transport systems

This paper compares the use of one-dimensional (1-D) and a three-dimensional (3-D) models to simulate the flow of a gas–solids mixture through a pipeline. Both models solve steady flow conservation equations for mass, momentum and energy. The implementation of each model is presented in terms of the changes made to the generic model in order to describe this type of flow. Performance data was obtained for a pneumatic conveying system used to convey pulverised fuel ash (PFA) in a power station. Each model was used to simulate the behaviour of this ash transfer line.     

Concurrent simulation of multibody systems coupled with stress–strain and heat transfer solvers

In the present work multibody 3-axis truck vehicle model coupled with submodels of suspension bodies is considered. Coupling the main model with submodels allows to perform simulation of multibody dynamics and non-stationary heat conduction and stress distribution processes in bodies simultaneously. High efficiency of parallel simulation on computer cluster is achieved using developed software based on MPI library.     

Generalized Helmert–Ledermann orthogonal matrices and rom simulation

Deterministic rectangular orthonormal matrices satisfying a hyper-plane constraint plays a central role in random orthogonal matrix (ROM) simulation. The multivariate skewness and kurtosis sampling properties are encrypted in a given orthonormal matrix. We consider a subclass of generalized Helmert–Ledermann (GHL) orthogonal matrices that have fixed last column, are generated by the Cayley transform, and satisfy the required hyper-plane constraint. The algebraic structure of GHL orthogonal matrices is determined. Simple and convenient skewness and kurtosis formulas are obtained. We exhibit an asymptotically growing range of variation for skewness and kurtosis, which points to an increased flexibility in ROM simulation.     

The use of simulation and case study†

Although statistics is a rational subject, it does not follow that students can or do learn statistics in a rational way. Students learn statistics in the pattern‐forming mode more than in the rational mode. The paper describes and compares the two modes, and identifies three conditions that prevent or discourage learning in the rational mode. The diagnosis of pattern‐forming de‐emphasizes mathematical derivations and proofs as a means of allowing students to understand statistical concepts. The primary recommendation is that the teacher should deliberately manipulate the pattern‐forming process. The underlying idea is for the teacher to view the process for what it means to the student.     

Local Convergence of Large Critical Multi-type Galton–Watson Trees and Applications to Random Maps

We show that large critical multi-type Galton–Watson trees, when conditioned to be large, converge locally in distribution to an infinite tree which is analogous to Kesten’s infinite monotype Galton–Watson tree. This is proven when we condition on the number of vertices of one fixed type, and with an extra technical assumption if we count at least two types. We then apply these results to study local limits of random planar maps, showing that large critical Boltzmann-distributed random maps converge in distribution to an infinite map.     

Performance analysis of an irreversible Miller cycle with considerations of relative air–fuel ratio and stroke length

The performance of an air standard Miller cycle is analyzed using finite-time thermodynamics. The results show that if compression ratio exceeds certain value, the power output first increases and then starts to decrease with increasing relative air–fuel ratio, while if compression ratio exceeds certain value, the power output decreases with increasing relative air–fuel ratio. The results also show that if compression ratio is less than certain value, the power output decreases with increasing stroke length, while if compression ratio exceeds certain value, the power output first increases and then starts to decrease with increasing stroke length. With further increase in compression ratio, the increase of stroke length results in decreasing the power output. The results obtained from this work can be helpful in the design and evaluation of practical Miller engines.     

Large time behavior of the isentropic compressible Navier–Stokes–Maxwell system

In this paper, we study the large time behavior of the isentropic compressible Navier–Stokes–Maxwell system introduced by Jiang and Li (Nonlinearity 25(6):1735–1752, 2012) in the whole space \({{\mathbb{R}}^3}\) when the initial data are a small perturbation of some given constant state. We obtain the desired result through taking the refined analysis on the time decay property and Green’s function of the linearized system. Moreover, we also obtain the optimal time rate of the solution.