Результаты поиска по 'the difference scheme':
Найдено статей: 72
  1. Nikitin I.S., Nikitin A.D.
    Multi regime model and numerical algorithm for calculations on various types quasi crack developing under cyclic loading
    Computer Research and Modeling, 2022, v. 14, no. 4, pp. 873-885

    A new method for calculating the initiation and development of narrow local damage zones in specimens and structural elements subjected to various modes cyclic loadings is proposed based on multi regime two criteria model of fatigue fracture. Such narrow zones of damage can be considered as quasi-cracks of two different types, corresponding to the mechanism of normal crack opening and shear.

    Numerical simulations that are aimed to reproduce the left and right branches of the full fatigue curves for specimens made from titanium and aluminum alloy and to verify the model. These branches were constructed based on tests results obtained under various modes and cyclic loading schemes. Examples of modeling the development of quasi-cracks for two types (normal opening and shear) under different cyclic loading modes for a plate with a hole as a stress concentrator are given. Under a complex stress state in the proposed multi regime model, a natural implementation of any considered mechanisms for the quasi-cracks development is possible. Quasi-cracks of different types can develop in different parts of the specimen, including simultaneously.

    Keywords: fatigue fracture, high cycle fatigue, very high cycle fatigue, multi regime model, damage equation, fracture criterion, quasi crack.
  2. Lobanov A.I., Mirov F.Kh.
    On the using the differential schemes to transport equation with drain in grid modeling
    Computer Research and Modeling, 2020, v. 12, no. 5, pp. 1149-1164

    Modern power transportation systems are the complex engineering systems. Such systems include both point facilities (power producers, consumers, transformer substations, etc.) and the distributed elements (f.e. power lines). Such structures are presented in the form of the graphs with different types of nodes under creating the mathematical models. It is necessary to solve the system of partial differential equations of the hyperbolic type to study the dynamic effects in such systems.

    An approach similar to one already applied in modeling similar problems earlier used in the work. New variant of the splitting method was used proposed by the authors. Unlike most known works, the splitting is not carried out according to physical processes (energy transport without dissipation, separately dissipative processes). We used splitting to the transport equations with the drain and the exchange between Reimann’s invariants. This splitting makes possible to construct the hybrid schemes for Riemann invariants with a high order of approximation and minimal dissipation error. An example of constructing such a hybrid differential scheme is described for a single-phase power line. The difference scheme proposed is based on the analysis of the properties of the schemes in the space of insufficient coefficients.

    Examples of the model problem numerical solutions using the proposed splitting and the difference scheme are given. The results of the numerical calculations shows that the difference scheme allows to reproduce the arising regions of large gradients. It is shown that the difference schemes also allow detecting resonances in such the systems.

    Keywords: grid, graph, telegraph equation, transport equation with drain, difference schemes, insufficient coefficients, linear programming.
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