Mass conservation and singular multicomponent diffusion algorithms

We investigate mass conservation in multicomponent diffusion algorithms. Usual diffusion matrices are indeed singular, i.e., noninvertible, because of mass conservation constraints. A consequence is that when all mass fractions are treated as independent unknowns-a widely used approach in complex chemistry reacting flow solvers-artificial singularities may appear in the governing equations. These singularities arise, for instance, with species flux boundary conditions or with steady flows involving stagnation points. In these situations, the Jacobian matrices of the discrete governing equations are singular. Modifications of the usual diffusion algorithms are introduced to eliminate these singularities. These modifications, of course, do not change the actual values of the diffusion velocities. Only their mathematical expressions are changed.