Keywords: numerical simulation, railways, non-destructive control, ultrasonic control, railway embankment control, wheel-rail contact, damaged wheel impact, wave propagation, grid-characteristic method, discontinuous Galerkin method.

There are many kinds of non-destructive railway testing techniques. This paper concentrates on the ultrasonic method. At present, this method is being actively developed. Great contributions to this development have been using computer simulation of physical processes (propagation of elastic waves) in material of the rail. It should be noted, that there are various approaches to conducting numerical experiments but in the majority of these papers the conducting of computer simulation was made using commercial closed-source software such as ABAQUS or ANSYS. The absence of a detailed understanding of the computational algorithms and the lack of possibility of estimating the result correctness significantly reduces the value of the received practical results. In this paper, the grid-characteristic approach to simulation of the process of non-destructive testing is discussed. Also we use the discontinuous Galerkin method. Hence complex software, using high-performance computer systems, permitting computer experiments, was developed, and the paper presents the first results of these calculations. The use of accumulated experience in this area will greatly accelerate the development of effective methods of non-destructive railway testing.

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