This file implements the time integration of a system of stochastic differential equations (SDEs), whose invariant is the Dirichlet distribution, with various constraints to model multi-material mixing process in turbulent flows.
In a nutshell, the equation integrated governs a set of scalars, , , , as
with parameter vectors , , and , and . Here is an isotropic vector-valued Wiener process with independent increments. The invariant distribution is the Dirichlet distribution, provided the parameters of the drift and diffusion terms satisfy
To keep the invariant distribution Dirichlet, the above constraint on the coefficients must be satisfied. For more details on the Dirichlet SDE, see https://doi.org/10.1155/2013/842981.
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