In this paper we consider the frictional (tangential) steady rolling contact problem. We confine ourselves to the simplified theory, instead of using full elastostatic theory, in order to be able to compute results fast, as needed for on-line application in vehicle system dynamics simulation packages. The FASTSIM algorithm is the leading technology in this field and is employed in all dominant railway vehicle system dynamics packages (VSD) in the world. The main contribution of this paper is a new version "FASTSIM2" of the FASTSIM algorithm, which is second-order accurate. This is relevant for VSD, because with the new algorithm 16 times less grid points are required for sufficiently accurate computations of the contact forces. The approach is based on new insights in the characteristics of the rolling contact problem when using the simplified theory, and on taking precise care of the contact conditions in the numerical integration scheme employed.

SUMMARYOften industrial codes for the numerical integration of the 2D shallow water equations are based on an Alternating Direction Implicit method. However, for large time steps these codes suffer from inaccuracies when dealing with a complex geometry or bathymetry. This reduces the performance considerably. In this paper a new method is presented in which these inaccuracies are absent, even for large time steps. The method is a fully implicit time integration method. In order to obtain linear systems that can be solved efficiently, we introduce a time splitting method. The resulting linear systems are solved iteratively by using the preconditioned Conjugate Gradients Squared method.

We construct a space-centered self-adjusting hybrid difference method for one-dimensional hyperbolic conservation laws. The method is linearly implicit and combines a newly developed minimum dispersion scheme of the first order with the recently developed second-order scheme of Lerat. The resulting method is unconditionally stable and unconditionally diagonally dominant in the linearized sense. The method has been developed for quasi-stationary problems, in which shocks play a dominant role. Numerical results for the unsteady Euler equations are presented. It is shown that the method is non-oscillatory, robust and accurate in several cases.

SUMMARYThe numerical solution of a single first-order conservation equation by a least-squares finite element method is considered. Isoparametric bilinear quadrilateral elements are used. The accuracy is studied numerically and it is shown that the discrete equations associated with nodal points on the boundaries should be modified in order to obtain an accurate numerical solution.

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