| Abstrakt: |
AbstractWith the example of solving some known modeling problems the fea-tures of constructing grids adapted to the solution of parabolic equations are consid-ered. Convection-diffusion problems are described by nonlinear Burgers and Buckley — Leverette equations. A detailed analysis of the differential approximations and numerical results shows that the idea of using an arbitrary time-dependent system of coordinates for adapted grid generation in combination with the principle of quasi-stationarity makes the dy-namic adaptation method universal, effective, and algorithmically simple. Universality is achieved due to the use of an arbitrary time-dependent system of co-ordinates that moves at a velocity determined by the unknown solution. This universal approach makes it possible to generate adapted grids for time-dependent problems of mathematical physics with various mathematical features. Among these features are large gradients, and propagation of weak and strong discontinuities in known nonlinear transfer problems. The efficiency is determined by automatically fitting the velocity of the moving nodes to the dynamics of the solution. The close relationship between the adaptation mechanism and the structure of parabolic equations allows one to automatically control nodes motion of nodes so that their trajectories do not intersect. The simplicity of the algorithm is achieved due to the general approach to the adaptive grid generation that is independent of the form and type of the differential equations. |
