Edwin A. H. Vollebregt

Assessing the accuracy of different simplified frictional rolling contact algorithms

This paper presents an approach for assessing the accuracy of different frictional rolling contact theories. The main characteristic of the approach is that it takes a statistically oriented view. This yields a better insight into the behaviour of the methods in diverse circumstances (varying contact patch ellipticities, mixed longitudinal, lateral and spin creepages) than is obtained when only a small number of (basic) circumstances are used in the comparison. The range of contact parameters that occur for realistic vehicles and tracks are assessed using simulations with the Vampire vehicle system dynamics (VSD) package. This shows that larger values for the spin creepage occur rather frequently. Based on this, our approach is applied to typical cases for which railway VSD packages are used. The results show that particularly the USETAB approach but also FASTSIM give considerably better results than the linear theory, Vermeulen–Johnson, Shen–Hedrick–Elkins and Polach methods, when compared with the ‘complete theory’ of the CONTACT program.

Solving conformal wheel–rail rolling contact problems

The stresses between railway wheels and rails can be computed using different types of contact models: simplified methods, half-space-based boundary element approaches and finite element models. For conformal contact situations, particularly the contact between flange root and rail gauge corner, none of these models work satisfactorily. Finite element methods are too slow, half-space approaches ignore the effects of conformality, and simplified approaches schematise the elasticity of the material even further. This paper presents a thorough investigation of the conformal wheel–rail rolling contact problem. We use CONTACTs boundary element approach together with numerical influence coefficients, that are computed using the finite element approach. The resulting method is fast and detailed and can be embedded into vehicle system dynamics simulation. The results indicate that the contact area is longer and narrower, with smaller area and reduced stiffness, than is predicted by the half-space approach. The predicted maximum pressures are increased by 30%. Finally the longitudinal and lateral forces changed up to 15% of the Coulomb maximum.

Large scale computing at Rijkswaterstaat

The Dutch Rijkswaterstaat uses simulation models extensively in carrying out its various tasks, among which are the protection of the country from flooding and the management of shipping routes and ports. Different applications of the models lead to large scale computations. Furthermore the continuing increase in level of detail of the simulations demands more and more computing power.In the past few years, Rijkswaterstaat/RIKZ, Delft University of Technology and VOR-tech Computing have developed and implemented techniques to make these large scale simulations possible. First the 3D shallow water model TRIWAQ has been parallelized. Then this parallel version has been extended to allow for different forms of domain decomposition. Finally also various on-line couplings with different models have been established.In this paper we give an overview of these developments and of our approach towards parallel computing that enabled us to carry out all of these developments in a single conceptual framework.

The Bound-Constrained Conjugate Gradient Method for Non-negative Matrices

Existing conjugate gradient (CG)-based methods for convex quadratic programs with bound constraints require many iterations for solving elastic contact problems. These algorithms are too cautious in expanding the active set and are hampered by frequent restarting of the CG iteration. We propose a new algorithm called the Bound-Constrained Conjugate Gradient method (BCCG). It combines the CG method with an active-set strategy, which truncates variables crossing their bounds and continues (using the Polak–Ribière formula) instead of restarting CG. We provide a case with n=3 that demonstrates that this method may fail on general cases, but we conjecture that it always works if the system matrix A is non-negative. Numerical results demonstrate the effectiveness of the method for large-scale elastic contact problems.

On the portability and efficiency of parallel algorithms and software

Abstract Parallel software development must face the fact that different architectures require different implementations. Flexibility in modifying parallel methods and software is necessary because the efficiency of algorithms is dependent on the characteristics of the target computer. Furthermore different parallel computers require different implementations of data in data-structures. The required flexibility is obtained by identifying abstraction levels and development steps in parallel algorithm and software development. The approach which is proposed ensures that all choices in the design are properly recognised and documented. As a result it is simple to compare the characteristics of a new parallel computer with the characteristics that are used in the software. In this way the development itself becomes more portable and thus less architecture dependent.

Multigrid with FFT smoother for a simplified 2D frictional contact problem

This paper aims to develop a fast multigrid (MG) solver for a Fredholm integral equation of the first kind, arising from the 2D elastic frictional contact problem. After discretization on a rectangular contact area, the integral equation gives rise to a linear system with the coefficient matrix being dense, symmetric positive definite and Toeplitz. A so-called fast Fourier transform (FFT) smoother is proposed. This is based on a preconditioner M that approximates the inverse of the original coefficient matrix, and that is determined using the FFT technique. The iterates are then updated by Richardson iteration: adding the current residuals preconditioned with the Toeplitz preconditioner M. The FFT smoother significantly reduces most components of the error but enlarges several smooth components. This causes divergence of the MG method. Two approaches are studied to remedy this feature: subdomain deflation (SD) and row sum modification (RSM). MG with the FFT + RSM smoother appears to be more efficient than using the FFT + SD smoother. Moreover, the FFT + RSM smoother can be applied as an efficient iterative solver itself. The two methods related to RSM also show rapid convergence in a test with a wavy surface, where the Toeplitz structure is lost.

Abstract Level Parallelization of Finite Difference Methods

A formalism is proposed for describing finite difference calculations in an abstract way. The formalism consists of index sets and stencils, for characterizing the structure of sets of data items and interactions between data items (“neighbouring relations”). The formalism provides a means for lifting programming to a more abstract level. This simplifies the tasks of performance analysis and verification of correctness, and opens the way for automatic code generation. The notation is particularly useful in parallelization, for the systematic construction of parallel programs in a process/channel programming paradigm (e.g., message passing). This is important because message passing, unfortunately, still is the only approach that leads to acceptable performance for many more unstructured or irregular problems on parallel computers that have non-uniform memory access times. It will be shown that the use of index sets and stencils greatly simplifies the determination of which data must be exchanged between different computing processes.

Using the GCel for simulation of flow in the continental shelf region

Abstract Accurate predictions of flows and transport in the continental shelf region can be obtained using a numerical simulation of the three dimensional shallow water equations. As more powerful computers become available, the grids that are used in these simulations can be much finer, making the results more reliable. This article describes a first implementation of existing simulation software on the GCel computer of SARA in Amsterdam. The modification of the algorithms is described and issues related to load balancing, communication and data distribution will be discussed. The results of the first experiments with this implementation show that the expected performance can be reached.

Parallel simulation of 3-D flow and transport models within the NOWESP project

Abstract In this paper, a short overview of project 3, “Advanced Flux Modelling”, in the NOWESP project of the MAST II programme is given. The computational requirements of large scale 3-D flow and transport models of the North-West European Shelf are considered. The possibilities and implications of massively parallel processors for the simulation of these models are discussed. We also present some of the results and experience obtained in parallelising the shallow water flow and transport models within the NOWESP project.

A Full Multigrid Method for Linear Complementarity Problems arising from Elastic Normal Contact Problems

AbstractThis paper presents a full multigrid (FMG) technique, which combines a multigrid method, an active set algorithm and a nested iteration technique, to solve a linear complementarity problem (LCP) modeling elastic normal contact problems. The governing system in this LCP is derived from a Fredholm integral of the first kind, and its coefficient matrix is dense, symmetric and positive definite. One multigrid cycle is applied to solve this system approximately in each active set iteration. Moreover, this multigrid solver incorporates a special strategy to handle the complementarity conditions, including restricting both the defect and the contact area (active set) to the coarse grid, and setting all quantities outside contact to zero. The smoother is chosen by some analysis based on the eigenvectors of the iteration matrix. This method is applied to a Hertzian smooth contact and a rough surface contact problem.