Transport algorithms for partially ionized and unmagnetized plasmas

A new formalism for the transport properties of partially ionized and unmagnetized plasmas is investigated from a computational point of view. Heavy particle transport expressions for shear viscosity, translational thermal conductivity, and thermal diffusion ratios are obtained from the solution of symmetric linear systems. Electron transport properties are also presented. A general Stefan–Maxwell equation and two approximate formulations deal with diffusion phenomenon. Well-posedness of the transport properties is established, provided that some conditions on the kinetic data are met. The mathematical structure of the transport matrices is readily used to build transport algorithms inspired by Ern and Giovangigli [J. Comput. Phys. 120 (1995) 105]. These algorithms rely either on a direct linear solver or on convergent iterative Krylov projection methods, such as the conjugate gradient. The Stefan–Maxwell matrix is singular and a mass conservation constraint completes the system of equations. A yet symmetric and non-singular Stefan–Maxwell matrix including the mass constraint is introduced for the direct method. A suitable projector associated with the singular form of the matrix is used for the iterative methods. An 11-species air mixture in local thermodynamic equilibrium at atmospheric pressure serves as benchmark to assess the physical model and numerical methods. Superiority of the conjugate gradient method with respect to the direct solver and approximate mixture rules found in the literature is demonstrated in terms of accuracy and computational cost.