Long Beach Harbor numerical analysis of harbor oscillations :

"February 1977."

Current United States practice for numerical analysis of dams : a report /

"February 1985."

OMNITAB : a computer program for statistical and numerical analysis /

Includes bibliographies and index.

Numerical analysis for a variable-order nonlinear cable equation

In this paper, a variable-order nonlinear cable equation is considered. A numerical method with first-order temporal accuracy and fourth-order spatial accuracy is proposed. The convergence and stability of the numerical method are analyzed by Fourier analysis. We also propose an improved numerical method with second-order temporal accuracy and fourth-order spatial accuracy. Finally, the results of a numerical example support the theoretical analysis.

Numerical analysis of the time variable fractional order mobile-immobile advection-dispersion model

Many physical processes exhibit fractional order behavior that varies with time or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider the time variable fractional order mobile-immobile advection-dispersion model. Numerical methods and analyses of stability and convergence for the fractional partial differential equations are quite limited and difficult to derive. This motivates us to develop efficient numerical methods as well as stability and convergence of the implicit numerical methods for the fractional order mobile immobile advection-dispersion model. In the paper, we use the Coimbra variable time fractional derivative which is more efficient from the numerical standpoint and is preferable for modeling dynamical systems. An implicit Euler approximation for the equation is proposed and then the stability of the approximation are investigated. As for the convergence of the numerical scheme we only consider a special case, i.e. the time fractional derivative is independent of time variable t. The case where the time fractional derivative depends both the time variable t and the space variable x will be considered in the future work. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical analysis of shape transition in graphene nanoribbons

Graphene nanoribbon (GNR) with free edges can exhibit non-flat morphologies due to pre-existing edge stress. Using molecular dynamics (MD) simulations, we investigate the free-edge effect on the shape transition in GNRs with different edge types, including regular (armchair and zigzag), armchair terminated with hydrogen and reconstructed armchair. The results show that initial edge stress and energy are dependent on the edge configurations. It is confirmed that pre-strain on the free edges is a possible way to limit the random shape transition of GNRs. In addition, the influence of surface attachment on the shape transition is also investigated in this work. It is found that surface attachment can lead to periodic ripples in GNRs, dependent on the initial edge configurations.

Three-dimensional off-design numerical analysis of an organic Rankine cycle radial-inflow turbine

Optimisation of organic Rankine cycles(ORCs for binary cycle applications could play a major role in determining the competitiveness of low to moderate renewable sources. An important aspect of the optimisation is to maximise the turbine output power for a given resource. This requires careful attention to the turbine design notably through numerical simulations. Challenges in the numerical modelling of radial-inflow turbines using high-density working fluids still need to be addressed in order to improve the turbine design and better optimise ORCs. Thispaper presents preliminary 3D numerical simulations of a high-density radial-inflow ORC turbine in sensible geothermal conditions. Following extensive investigation of the operating conditions and thermodynamic cycle analysis, therefrigerant R143a is chosen as the high-density working fluid. The 1D design of the candidate radial-inflow turbine is presented in details. Furthermore, commercially-available software Ansys-CFX is used to perform preliminary steady-state 3D CFD simulations of the candidate R143a radial-inflow turbine for a number of operating conditions including off-design conditions. The real-gas properties are obtained using the Peng–Robinson equations of state.The thermodynamic ORC cycle is presented. The preliminary design created using dedicated radial-inflow turbine software Concepts-Rital is discussed and the 3D CFD results are presented and compared against the meanline analysis.

A poroviscohyperelastic model for numerical analysis of mechanical behavior of single chondrocyte

The aim of this paper is to utilize a poroviscohyperelastic (PVHE) model which is developed based on the porohyperelastic (PHE) model to explore the mechanical deformation properties of single chondrocytes. Both creep and relaxation responses are investigated by using FEM models of micropipette aspiration and AFM experiments, respectively. The newly developed PVHE model is compared thoroughly with the SnHS and PHE models. It has been found that the PVHE can accurately capture both creep and stress relaxation behaviors of chondrocytes better than other two models. Hence, the PVHE is a promising model to investigate mechanical properties of single chondrocytes.

Numerical analysis for the time distributed-order and Riesz space fractional diffusions on bounded domains

Subdiffusion equations with distributed-order fractional derivatives describe some important physical phenomena. In this paper, we consider the time distributed-order and Riesz space fractional diffusions on bounded domains with Dirichlet boundary conditions. Here, the time derivative is defined as the distributed-order fractional derivative in the Caputo sense, and the space derivative is defined as the Riesz fractional derivative. First, we discretize the integral term in the time distributed-order and Riesz space fractional diffusions using numerical approximation. Then the given equation can be written as a multi-term time–space fractional diffusion. Secondly, we propose an implicit difference method for the multi-term time–space fractional diffusion. Thirdly, using mathematical induction, we prove the implicit difference method is unconditionally stable and convergent. Also, the solvability for our method is discussed. Finally, two numerical examples are given to show that the numerical results are in good agreement with our theoretical analysis.

Numerical analysis of a new space-time variable fractional order advection-dispersion equation

Many physical processes appear to exhibit fractional order behavior that may vary with time and/or space. The continuum of order in the fractional calculus allows the order of the fractional operator to be considered as a variable. In this paper, we consider a new space–time variable fractional order advection–dispersion equation on a finite domain. The equation is obtained from the standard advection–dispersion equation by replacing the first-order time derivative by Coimbra’s variable fractional derivative of order α(x)∈(0,1]α(x)∈(0,1], and the first-order and second-order space derivatives by the Riemann–Liouville derivatives of order γ(x,t)∈(0,1]γ(x,t)∈(0,1] and β(x,t)∈(1,2]β(x,t)∈(1,2], respectively. We propose an implicit Euler approximation for the equation and investigate the stability and convergence of the approximation. Finally, numerical examples are provided to show that the implicit Euler approximation is computationally efficient.

Numerical analysis for the interlayer toughening of piezoelectric smart composite plate

The piezoelectric composite material could engender stress concentration resulting from small cracks during layers easily, as the cracks growth will lead to the failure of the whole structure. In this paper, a finite element model for piezoelectric composite materials by ABAQUS including interlayer crack was established, and the J integral and crack tip stress of different types PZT patches were calculated by using the equivalent integral method. Then, the J integral for adhesive layers with different thickness, elastic modulus considering and not considering piezoelectricity was investigated. The results show that the J integral of mode I, II reduces with thicker adhesive layer and lower elastic modules, and the J integral of mode II decreases more sharply than that of mode I.