Abstract

This work numerically analyzes blow-up phenomena in solutions to a parabolic partial differential equation with a convection term, subject to non-homogeneous Neumann boundary conditions and strictly positive initial data. This problem represents a turbulence model of fluid flows. We establish conditions under which the semi-discrete spatial formulation of the continuous problem blows up in finite time and we estimate the corresponding semi-discrete blow-up time. We also prove that the semi-discrete blow-up time converges to real one, when the spatial discretization step tends to zero. From fully discretized schemes, we have developed algorithms that have allowed us to obtain good approximations of the blow-up time and other numerical results to illustrate our analysis.

This work is licensed under a Creative Commons Attribution 4.0 License.