Linearized Θ-methods part II: Reaction-diffusion equations Original Research Article

Second-order accurate in space, partially-linearized, triangular and diagonal (Θ-methods for reaction-diffusion equations, which employ either a standard or a delta formulation, are developed and applied to both the study of a system of one-dimensional, reaction-diffusion equations with algebraic nonlinear reaction terms and the propagation of a one-dimensional, confined, laminar flame. These methods require the solution of tridiagonal matrices for each dependent variable, and either uncouple or sequentially couple the dependent variables at each time step depending on whether they are diagonally- or triangularly-linearized techniques, respectively. Partially-linearized, diagonal methods yield larger errors than partially-linearized, triangular techniques, and the accuracy of the latter depends on the time step, standard or delta formulation, implicitness parameter and the order in which the equations are solved. Fully- and partially-linearized, operator-splitting methods for reaction-diffusion equations are also developed; the latter provide explicit expressions for the solution of the reaction operator.