V. I. Agoshkov

Shape Design in Aorto-Coronaric Bypass Anastomoses Using Perturbation Theory

In this paper we present a new approach in the study of aorto-coronaric bypass anastomoses configurations based on small perturbation theory. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary. The aim is to provide design indications in the perspective of future development for prosthetic bypasses.

A Mathematical Approach in the Design of Arterial Bypass Using Unsteady Stokes Equations

In this paper we present an approach for the study of Aorto-Coronaric bypass anastomoses configurations using unsteady Stokes equations. The theory of optimal control based on adjoint formulation is applied in order to optimize the shape of the zone of the incoming branch of the bypass (the toe) into the coronary according to several optimality criteria.

Mathematical and numerical modelling of shallow water flow

This paper deals with shallow water equations. We discuss the mathematical model, the admissible boundary conditions, some popular numerical methods in the specialized literature, as well as we propose new approaches based on fractional step and finite element methods.

Recent developments in the numerical simulation of shallow water equations I: boundary conditions

Abstract Shallow water equations (briefly, SWE) provide a model to describe fluid dynamical processes of various nature, and find therefore widespread application in science and engineering. A rigorous mathematical analysis is not available, unless for few specific cases under strict assumptions on the problems data. In particular, the issue of which kind of boundary conditions are allowed is not completely understood yet. Here we investigate several sets of boundary conditions of physical interest that are admissible from the mathematical viewpoint. By that we mean that, when plugged into the integral form of SWE, these boundary conditions allow the proof of a priori estimates for the unknowns of physical interest: the velocity field and the elevation on the fluid (or its pressure). In our investigation we consider the most general case in which the physical boundary is partitioned into two sets: one closed (this is typically a coast or a shore), the other open (this is a virtual boundary delimiting the domain of investigation). In the latter we further distinguish among inflow and outflow boundary. Several kinds of conditions are investigated on each boundary component. The paper is concluded showing how to achieve a priori estimates corresponding to three different choices of boundary conditions. The correct treatment of boundary terms is crucial for both mathematical and numerical analysis of SWE. The characterization of the set of boundary conditions of physical interest that are mathematically admissible is important in view of the numerical simulation of this kind of phenomena. This paper is the first part of an investigation that the authors have carried out in this field. A second one shows how to implement these boundary conditions in the framework of discrete methods based on a finite element approximation in space, and several kind of time-marching techniques [11]. In particular, the a priori estimates obtained throughout this paper are extended in order to show stability properties for the approximate solution. Numerical experiments based on test cases corresponding to the various sets of boundary conditions considered here are presented in [10,12].

Observational data assimilation in the problem of Black Sea circulation and sensitivity analysis of its solution

The problem of the variational data assimilation of the sea-surface temperature for the model of the Black Sea dynamics has been formulated and numerically studied to reproduce surface heat fluxes. An analysis of sensitivity of the optimal solution to errors in observation data has been conducted. The results of numerical experiments have been presented.

Problems of Variational Assimilation of Observational Data for Ocean General Circulation Models and Methods for Their Solution

Problems of the variational assimilation of satellite observational data on the temperature and level of the ocean surface, as well as data on the temperature and salinity of the ocean from the ARGO system of buoys, are formulated with the use of the global three-dimensional model of ocean thermodynamics developed at the Institute of Numerical Mathematics, Russian Academy of Sciences (INM RAS). Algorithms for numerical solutions of the problems are developed and substantiated, and data assimilation blocks are developed and incorporated into the global three-dimensional model. Numerical experiments are performed with the use of the Indian Ocean or the entire World Ocean as examples. These numerical experiments support the theoretical conclusions and demonstrate that the use of a model with an assimilation block of operational observational data is expedient.

Numerical algorithm for variational assimilation of sea surface temperature data

The problem of variational assimilation of sea surface temperature data is formulated and studied. An algorithm for solving the problem is developed. Numerical results are presented.

Modeling Black Sea circulation with high resolution in the coastal zone

We present a numerical model of Black Sea circulation based on primitive equations with improved spatial resolution in the coastal zone. The model equations are formulated in a two-pole orthogonal coordinate system with arbitrary locations of the poles and a vertical σ coordinate. Increased horizontal resolution is gained by displacing the pole into the vicinity of the separated subdomain. The problem is solved over a grid with a variable step. The northern coordinate pole is displaced to the vicinity of Gelendzhik; the grid step varies from 150 m in the coastal zone to 4.6 km in the main basin. We simulated the fields of currents, sea level, temperature, and salinity under the given atmospheric forcing in 2007. The model is capable of reproducing the large-scale Black Sea circulation and submesoscale variations in the coastal currents.

A numerical algorithm of variational data assimilation for reconstruction of salinity fluxes on the ocean surface

Abstract A problem of variational data assimilation concerning salinity on the ocean surface is formulated and studied. A solution algorithm for this problem is developed. The results of numerical experiments are presented.

A new interpolation method for observation data obtained from ARGO buoys system

Abstract Experimental and observation data obtained from various sources are used in studying and solving many problems of geophysical hydrodynamics. A method for interpolation of observation data on regular grids is presented in the paper. The method takes into account the transport of data by currents and allows one to improve the accuracy of interpolation of these observation data fields by introducing ‘pseudo observations’.