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Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics

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Abstract

Techniques that improve the accuracy of numerical solutions and reduce their computational costs are discussed as applied to continuum mechanics problems with complex time-varying geometry. The approach combines shock-capturing computations with the following methods: (1) overlapping meshes for specifying complex geometry; (2) elastic arbitrarily moving adaptive meshes for minimizing the approximation errors near shock waves, boundary layers, contact discontinuities, and moving boundaries; (3) matrix-free implementation of efficient iterative and explicit–implicit finite element schemes; (4) balancing viscosity (version of the stabilized Petrov–Galerkin method); (5) exponential adjustment of physical viscosity coefficients; and (6) stepwise correction of solutions for providing their monotonicity and conservativeness.

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Authors and Affiliations

  1. Institute for Problems of Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, korp. 1, Moscow, 119526, Russia

    N. G. Burago

  2. Institute for Computer-Aided Design, Russian Academy of Sciences, ul. Vtoraya Brestskaya 19/18, Moscow, 123056, Russia

    I. S. Nikitin & V. L. Yakushev

Authors
  1. N. G. Burago
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  2. I. S. Nikitin
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  3. V. L. Yakushev
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Correspondence to N. G. Burago.

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Dedicated to the memory of O.M. Belotserkovskii

Original Russian Text © N.G. Burago, I.S. Nikitin, V.L. Yakushev, 2016, published in Zhurnal Vychislitel’noi Matematiki i Matematicheskoi Fiziki, 2016, Vol. 56, No. 6, pp. 1082–1092.

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Burago, N.G., Nikitin, I.S. & Yakushev, V.L. Hybrid numerical method with adaptive overlapping meshes for solving nonstationary problems in continuum mechanics. Comput. Math. and Math. Phys. 56, 1065–1074 (2016). https://doi.org/10.1134/S0965542516060105

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  • DOI: https://doi.org/10.1134/S0965542516060105

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