Volume 22, Issue 1

In this paper we propose a numerical method for solving nonstationary Maxwell equations on unstructured triangular grids, which is based on the finite volume method. We give the results of test calculations which confirm the second order of convergence of the method both for homogeneous media and media with space-variable dielectric permittivity.

In this paper we consider numerical methods for solving three-dimensional mixed boundary value problems for the complex Helmholtz equation describing electromagnetic fields with a harmonic time dependence. We propose nondivergent finite volume approximations on parallelepiped and tetrahedral grids, which are based on elementwise technologies calculating local balance matrices and assembling a global matrix. For the iterative solution of the obtained real system of linear algebraic equations (SLAE) with a nonsymmetric sparse high-order matrix we describe a preconditioned semi-conjugate residual method.We give results of numerical experiments for a set of model problems on a sequence of denser grids, which demonstrate the second order of accuracy of grid solutions and a high rate of convergence of iterative processes.

In this paper a two-step iterative method for solving the corresponding grid system is proposed for nonconforming finite element approximations of a 3D problem in the elasticity theory. We construct a preconditioner based on the transition from an elasticity operator to the grid Laplace operator, the diagonalization of the matrix for tangential displacements, and the inner Chebyshev procedures for normal displacements. We study the method theoretically and experimentally.

In this paper we describe results obtained in numerical investigation of the mechanism of tsunami generation by a moving submerged landslide which is simulated by a solid body sliding down a slope. The authors perform complex multiparameter calculations by algorithms based on the hierarchy of wave hydrodynamics models comprising shallow water equations and full hydrodynamical equations of an ideal fluid. We investigate the crucial dependences of the wave formation process on the length and thickness of the landslide, its bedding depth, and the law of motion. A comparison of solutions obtained by the approximate and full models allowed us to assess the degree of impact of the vertical flow structure and specify the domain of applicability of the approximate models.

In this paper we present numerical models of dynamics of a momentumless turbulence wake behind a body of revolution, which are based on improved second- and third-order turbulence models. We compare data of numerical experiments with experimental data.