Convergence Of Numerical Simulations Research Articles

The Impact of Numerical Parameters on the Resistance Characteristics of a Container Ship at the Model and Full Scale

Computational Fluid Dynamics (CFD) is a powerful tool used to predict the resistance characteristics of a ship. However, it is important to determine the numerical and modelling errors to assure accurate results. The aim of this study is the investigation of the impact of different numerical parameters on the total resistance, wave pattern and ship motion in numerical simulations at the model and full scale. These include the turbulence model and discretization schemes for convection, gradient and temporal terms within the governing equations. The numerical model used in numerical simulations is based on Reynolds Averaged Navier-Stokes (RANS) equations which are discretized using the Finite Volume Method (FVM). To locate and track the free surface, the Volume of Fluid (VOF) method is employed. The Grid Convergence Index (GCI) method is used for the verification study. The obtained results show that the selection of the discretization scheme for temporal term does not have impact on the median value of the total resistance and that the first-order scheme assures faster convergence in numerical simulations at the full scale. A higher portion of the frictional resistance in the total resistance is obtained with numerical simulations at the model scale in comparison to the full scale.

Determining initial tension of carrying cable in nonlinear analysis of bi-cable ropeway – Case study

This paper presents a computational approach dedicated to determining the initial tension of the carrying cable of a bi-cable ropeway under in-service moving load in numerical analyses. A continuous model of a multi-span inclined cable pre-tensioned by a counterweight is considered and changes in geometry are found to be the source of nonlinearity in the cable behaviour. Special attention is paid to the influence of nonlinear effects on the displacement state and axial forces. The main part of numerical research is preceded by tests of the convergence of solutions due to the applied discretisation method. In the first step an original computational algorithm is used to verify the initial tension of the cable estimated on the basis of a simplified formula for a single-span cable. In a static analysis of cable and counterweight displacements, the linear and nonlinear solutions are compared depending on different values of the initial cable tension. The problem of the solutions’ convergence in numerical simulations regarding the influence of nonlinearity is also discussed. Afterwards a quantitative dynamic analysis is performed to assess the impact of nonlinear effects on representative dynamic responses of the structure. The need to reduce the level of these effects and vibration amplitudes becomes clearly evident. In this context the recommended value of the initial cable tension is determined for engineering application and a limit level of transverse cable displacements is proposed. The presented concept of numerical investigations for determining the initial cable tension in a nonlinear analysis can be useful for practical calculations of ropeway structures.

Formula omitted] improvement of 2D [formula omitted] lattice SYM theory

We perform a tree-level O(a) improvement of two-dimensional N=(2,2) supersymmetric Yang–Mills theory on the lattice, motivated by the fast convergence in numerical simulations. The improvement respects an exact supersymmetry Q which is needed for obtaining the correct continuum limit without a parameter fine tuning. The improved lattice action is given within a milder locality condition in which the interactions are decaying as the exponential of the distance on the lattice. We also prove that the path-integral measure is invariant under the improved Q-transformation.

Correction scheme for point-particle models applied to a nonlinear drag law in simulations of particle-fluid interaction

Drag laws for particles in fluids are often expressed in terms of the undisturbed fluid velocity, defined as the fluid velocity a particle sees before its disturbance develops in the fluid. In two-way coupled point-particle simulations the information from the undisturbed state is not available and must be approximated using the disturbed velocity field. ([Horwitz, J. A. K. & Mani, A. 2016 Accurate calculation of stokes drag for point-particle tracking in two-way coupled flows. Journal of Computational Physics318, 85–109]) recently developed a procedure to estimate the undisturbed velocity for particles moving at low Reynolds number and obeying the linear Stokes drag law. Using this correction, convergence of numerical simulations was demonstrated to match the expected physical behavior for a range of canonical settings. In this paper we examine this correction scheme for particles moving at finite Reynolds number, by considering the nonlinear Schiller–Naumann drag law. Our results indicate that a linear correction can significantly improve prediction of drag force up to particle Reynolds number of about 10. Additionally, we present an investigation of the impact of this correction when applied to simulations of forced homogeneous turbulent particle-laden flows to further demonstrate the importance of modelling the undisturbed fluid velocity. While the shapes of particle acceleration and Reynolds number pdfs are not sensitive to correcting for the undisturbed fluid velocity, we show that an uncorrected scheme can result in significant under-prediction of the mean particle Reynolds number and standard deviation of particle acceleration. Furthermore, examination of particle radial distribution function reveals modest enhancements in preferential concentration predicted by the correction scheme (for St > 1). Our investigations of turbulent flows indicate the undisturbed fluid velocity correction to be more important for particles with larger size, while the Stokes number dependence is more complicated. The correction procedure shows a greater difference in particle slip velocity at higher Stokes numbers but more enhancement in preferential concentration at lower Stokes numbers. Finally, we propose a regime diagram to guide scheme selection for point-particle modelling.

Simulation and validation of disbond growth in co-cured composite skin–stringer specimens using cohesive elements

Separation of skin and stringer is likely to be a failure mode in co-cured composites stiffened panels where there is considerable out-of-plane deformation. Such deformations are possible when a stiffened skin structure is loaded in compression/shear beyond buckling or in structures which contain a disbond/delamination at the skin–stringer interface. Prediction of damage initiation and progressive growth in numerical simulations require parameters such as interface fracture toughness which have to be obtained through specimen tests. Since interface toughness is generally mode dependent, this study deals with the design and testing of three different configuration of blade stiffened co-cured composite skin–stringer specimens under mode-I and mode-II dominated loading. Finite element numerical models are developed using three-dimensional cohesive elements to predict the disbond growth under mode-I and mode-II dominated loading. The work also addresses the complexities in the convergence of numerical simulations that arise due to cohesive elements. A systematic way to obtain the best values for cohesive element parameters while finding a balance between accuracy of the results, computation time and numerical stability is presented. The present cohesive element modelling and analysis methodology successfully predicted the disbond growth in skin–stringer specimen and can be used to predict disbond/delamination onset or growth in composite stiffened structures subjected to high bending.

A calculating method of tube constants of ductile fracture criteria in tube free bulging process based on M-K theory

The purpose of this work was to obtain the accurate constants in ductile fracture criteria based on the M-K theory, which determined the condition of convergence in numerical simulations and predicted the ductile fracture during the tube free bulging process. In this paper, the equivalent stress was analyzed based on the M-K theory, and the constitutive equation of the tube free bulging was established. The ductile fracture criterion constants were obtained by the integral on the basis of the Freudenthal, Normalized C&L and Oyane theories. The comparison between the experimental and the simulation results regarding the free bulging, indicated that the Oyane ductile fracture criterion was more precise than the other criteria by the perimeter increase trend, the burst locations of the risky area and the crack length. The burst defects prediction became significantly accurate by the Oyane ductile fracture criterion utilization based on the M-K theory.

A corrected smoothed particle hydrodynamics approach to solve the non-isothermal non-Newtonian viscous fluid flow problems

In this paper, a corrected smoothed particle hydrodynamics (SPH) method is proposed to solve the problems of non-isothermal non-Newtonian viscous fluid. The proposed particle method is based on the corrected kernel derivative scheme under no kernel derivative and incompressible conditions, which possesses higher accuracy and better stability than the traditional SPH method. Meanwhile, a temperature-discretization scheme is deduced by the concept of SPH method for the purpose of precisely describing the evolutionary process of the temperature field. Reliability of the corrected SPH method for simulating the non-Newtonian viscous fluid flow is demonstrated by simulating the isothermal Poiseuille flow and the jet fluid of filling process; and the validity and accuracy of the proposed SPH discrete scheme in a temperature model for solving the non-isothermal fluid flow are tested by solving the non-isothermal Couette flow and 4:1 contraction flow. Subsequently, the proposed corrected SPH method combined with the SPH temperature-discretization scheme is tentatively extended to include the simulation of the non-isothermal non-Newtonian viscous free-surface flows in the ring-shaped and C-shaped cavities. Especially, the convergence of numerical simulations is analyzed, and the influences of heat flow parameters on the temperature and fluid flow at different positions are discussed.

Mathematical and biological models of blood coagulation

Mathematical and biological models of blood coagulation

Accelerated convergence in numerical simulations of surface supersaturation for crystal growth in solution under steady-state conditions

This is an investigative paper which reports the results of comparisons of two numerical techniques for the solution of the Burton Cabrera and Frank (BCF) equation for the growth on crystal surfaces under steady state conditions. A successive over-relaxation (SOR) scheme for the equivalent finite difference equation gives rapid convergence to the static solution. It is known that a suitable choice of scattering parameters in a transmission line matrix (TLM) network analogue of the Laplace equation yields ultra-fast convergence. The results of numerical experiments which are reported here suggests that a similar situation also applies to the solution of the Poisson equation with shunt losses (the BCF equation), although the choice of optimum conditions appears to be different for different spatial positions within the solution space. Copyright © 2005 John Wiley & Sons, Ltd.