Тип публикации: научное издание
Год издания: 2020
Идентификатор DOI: 10.1007/978-3-030-38870-6_43
Аннотация: Mathematical models of the dynamics of elastic-plastic, granular, and porous media are formulated as variational inequalities for hyperbolic operators with constraints describing the transition to a plastic state and different resistance of a material to tension and compression. Based on this, the problem of generalized solutions wПоказать полностьюith plastic shock waves is analyzed, integral estimates in characteristic cones of an operator are constructed, which guarantee the uniqueness and continuous dependence on initial data of the solutions of the Cauchy problem and boundary value problems with dissipative boundary conditions. Shock-capturing algorithms, suitable for computation of solutions with singularities such as strong discontinuities and discontinuities of displacements of a medium, are developed that satisfy the properties of monotonicity and dissipativity at the discrete level.
Журнал: Continuum Mechanics, Applied Mathematics and Scientific Computing: Godunov's Legacy: A Liber Amicorum to Professor Godunov
Номера страниц: 329-335
Издатель: Springer International Publishing