Numerical Solution of Free Boundary Problems for One-Dimensional Convection-Diffusion Equation.
Abstract:
Implicit difference scheme with second order of accuracy both in time and in space is constructed for linear convection - diffusion equation ∂ u/∂ t + c ∂ u/∂ x = μ ∂ 2u/∂ x2 . Moving grids are used. Position of a free boundary coincides with a line of grid. Convergence of the difference scheme is examined with the help of analytical solution of a free boundary problem for this equation. It is shown that the algorithm provides second order of accuracy both for solution of the problem and for position of the free boundary.
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
