Liquid antimony anode solid oxide fuel cell (LAA-SOFC) is a clean and efficient carbon/hydrocarbon-based power generation technology. Liquid metal anodes have better transport properties and hold stable even with solid carbon or complex fuel oil. Antimony (Sb) and antimony oxide (Sb2O3) are both in the liquid state at the SOFC working temperature, avoiding solid oxide formation at the anode-electrolyte interface. In this study we address convection flow of the Sb-Sb2O3 liquid-liquid phase in the anode, which is coupled with other physic-chemical phenomena. The physical model and the mathematical formulation, being treated numerically, include equations for two-phase fluid flow of Sb and Sb2O3, electric field and current, heat transfer, with taking into account the Joule heating and the heat released or consumed by chemical reactions, and production of Sb and Sb2O3 by reduction and oxidation reactions, respectively. The governing equation are discretized by the finite volume method with the three-time level projection scheme used for the time-dependent calculations. Most of the scheme are fully conservative, except the temperature convection term, for which the second order UPWIND scheme is applied. Motion of interface separating the two phases is modeled using the volume of fluid (VOF) method. The computations start from an initial state, in which most of the anode volume is occupied by Sb, while a small portion of its upper part is filled by lighter Sb2O3. The oxidation reaction takes place at the electrolyte-anode boundary. The reduction reaction happens inside the upper part of the anode, where carbon fuel is assumed to be supplied. During the time evolution, the amounts of Sb and Sb2O3 together with the interface arrive to the time-dependent asymptotic regime, in which production of Sb and Sb2O3 become balanced over the oscillation period. The velocity, temperature, concentration and electric potential field are monitored during the whole time evolution process. When changes in the total system volume, which takes place owing to the chemical reactions, is taken into account, the calculated oscillation period becomes closer to the results of a model experiment.