Monte Carlo implementation and analytic solution of an inert-scalar turbulent-mixing test problem using a mapping closure

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Abstract
A simple generalization, using a time‐dependent Gaussian scalar field, of a mapping closure recently proposed by Chen et al. [Phys. Rev. Lett. 63, 2657 (1989)] to model molecular mixing, enhanced by turbulent straining, for a fluctuating scalar field is presented and Monte Carlo implemented. An arbitrary parameter β allows the adjustment of the Gaussian‐scalar dissipation rate; the actual scalar field evolution is, however, independent of β. An analytic solution is obtained for the turbulent mixing of cells with two different values of the scalar content and simple symmetric initial conditions. Numerical results for this problem are produced, combining the Monte Carlo simulation and the analytic solution, in order to show the feasibility of this technique and its accuracy. Future extensions are outlined.