Numerical solution of continuity equation with a flux non-linearly depending on the density gradient

An approach to integrate transport equations with fluxes being complex non-linear functions of physical parameters and their gradients, as it is predicted by theoretical models for micro-instabilities in plasma, is proposed. This approach operates without any splitting of the flux on diffusive and convective components often involved in transport calculations. As an example, computations of the density profile in a stationary state and during dynamic evolution are done with the Weiland’s transport model. The results obtained by the proposed method and a conventional one with a flux splitting are compared.