Numerical Modeling of Finite Amplitude Convection of Liquids Subjected to Unipolar Injection

The unipolar injection stability problem is characterized by a hysteresis loop between nonlinear and linear stability criteria. The problem of determining the corresponding finite amplitude convective solution is investigated for rolls in the weak injection case, taking into account the peculiarities of the charge conservation equation and the possible nonstationary character of the flow. The results of three different approaches (finite difference method, approximate analytical solution, and particle-type method) are presented and discussed.