Volume 23, Issue 6

We consider a method for solving the system of equations of tidal dynamics based on approaches of classical splitting method and the theory of iterative processes. The statement of the problem is discussed when ‘pole points’ belong to computational domain. The numerical experiments are presented taking into account the real domain of the World Ocean, bottom topography, and tidal potential.

Numerical analysis of the evolution of a momentumless turbulent wake in a linearly stratified medium has been performed using mathematical models based on improved representations of ternary correlations of turbulent pulsing of the velocity and density fields. The results of calculations are compared to experimental data.

This paper presents a method for the calculation of the tsunami wave runup on an actual coast. This method consists in preliminary study of peculiarities of wave patterns near the coast for a series of simplified model water areas inheriting the basic characteristics of the considered fragment of the coastal zone and the use of the obtained results for the interpretation of the complicated runup pattern for a real coast. The results presented here are related to modelling tsunami waves runup on a part of the coast of the Bay of Bengal.

This paper deals with asymptotically correct methods to evaluate the local and global errors of Nordsieck formulas applied to ordinary differential equations. It extends naturally the results developed by Kulikov and Shindin [ Comp. Math. Math. Phys. (2000) 40 , 1255–1275] in local and global error computation of multistep methods, but shows that Kulikov and Shindin's technique becomes more complicated when implemented in numerical methods, for which the concepts of consistency and quasi-consistency are not equivalent (see Skeel [ SIAM J. Numer. Anal. (1976) 13 , 664–685]). A new property termed super quasi-consistency is introduced and special cases of Nordsieck formulas with cheaper error estimation are found. Numerical examples are included to confirm practically the theory presented in this paper.

A parallel algorithm utilizing the method of direct statistical modelling for approximate solution of the nonlinear coagulation equation in the spatially inhomogeneous case is presented in the paper. The algorithm is based on the method of majorant frequency. The algorithm can be implemented on parallel computers with distributed memory and with GRID systems. Variances for the estimates of statistical modelling and numerical calculation cost of the parallel algorithm are studied.

Two finite-difference schemes are proposed in the paper for the calculation of a viscous incompressible Bingham fluid flow. The Duvaut–Lions variational inequality is considered as a mathematical model of the medium. One of the finite-difference schemes is a generalization of the well-known MAC scheme on staggered grids. The other scheme uses one grid for approximation of all velocity components and another grid for all components of the rate of deformation tensor and pressure. A special stabilizing term is introduced into this scheme, which provides stability and preserves the second order of convergence of the scheme. Additional consistency conditions for grid operators are introduced, which are necessary for the correctness of the difference method. The numerical solution of the problem of the Bingham fluid flow in a cavity is considered as a model example.