Authors & Affiliations
Shcherbakov S.I.
A.I. Leypunsky Institute for Physics and Power Engineering, Obninsk, Russia
Shcherbakov S.I. – Senior Researcher, A.I. Leypunsky Institute for Physics and Power Engineering. Contacts: 1, pl. Bondarenko, Obninsk, Kaluga region, Russia, 249033. Tel.: +7(910)513-99-40; e-mail:
Abstract
The work is devoted to improving the numerical schemes for the dynamics of vector fields (fluid mechanics, electromagnetic field). The goal - reducing the time spent in solving the time-dependent problems through the use of large time steps. It is proposed to use an additional vector field, which together with the calculated changes, provides execution of incompressibility conditions of continuum - prevents the appearance of false mass, charge, of breaks of continuum, and physically corresponds to the rapid movement of perturbations (rate of light or sound), that are ended within a large time step. The equations system of vector field is complemented by equations of secondary disturbances calculation. This is the difference in the formulation of the problem in discrete and continuous time. This scheme leads to new concepts in the analysis. The vector field changes at each point of the region are divided into primary and secondary. Primary changes - it is local changes in the intensity of sources and time derivatives of vectors (from equations or external conditions). The primary change in one point immediately generates secondary (induced) changes in the entire region. At each point in the field, the secondary changes from various causes is combined additively. From primary disturbances in the small region are generated the specific elementary structures - O, F, C fields. These structures make it possible to simplify the analysis of the processes and to identify the feedbacks and, in the future, understand the causes of non-stationary periodic phenomena in the flow of liquid. Accounting of induced changes of vector field in the numerical calculation allows the use of large time steps.
Keywords
numerical simulation, Maxwell's equations, Navier-Stokes equations, time-dependent vector field, discrete time, a large time step, induced secondary changes, the basic structure of the field
Article Text (PDF, in Russian)
UDC 519.63