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The paper generalizes to the three-dimensional case the previously proposed two-dimensional mathematical model of the motion of a plasma formation in a constant transverse magnetic field. The complete system of single-fluid magnetogasdynamic approximation of the equations of the hydrodynamic method for plasma description under conditions of local thermodynamic equilibrium is simplified in the electromagnetic part. Instead of solving the complete system of Maxwell’s equations, Ohm’s integral law is applied to the conducting region with usage of empirical data. Earlier studies in a two-dimensional version of this model as applied to the problem of describing the motion of an arc showed its effectiveness and efficiency for the class of problems under consideration. The simulation results with proposed extended model are compared with previously obtained calculated and experimental data. Main integral and local features of flow structure are highlighted.

Different numerical algorithms for the solution of a class of unsteady convection‐diffusion‐reaction (CDR) equations are presented and compared in this paper. The fully implicit in time discretizations are usually preferred because they are unconditionally stable for linear problems. However, when implicit discretization is used for nonlinear problems, iterations over the nonlinearity have to be performed. Picard (simple linearization) or Newton's methods can be used for this purpose. An alternative to the fully implicit discretization is fractional time‐step methods, e.g. splitting with respect to physicochemical processes. The study of the latter class of discretization is especially interesting in the case when only the reactive term contains nonlinearity, while the convection and diffusion operators are linear. The CDR models used to describe processes in catalytic filters belong to this class. Numerical experiments for CDR equation with controllable stiffness of reaction term for different transport regimes, which are described by Peclet and Damkohler numbers are demonstrated and analyzed.