System of number-fraction beta SDEs.
In a nutshell, the equation integrated governs a set of scalars, , , as
with parameter vectors , , and . This is the same as in DiffEq/Beta.h. Here is an isotropic vector-valued Wiener process with independent increments. The invariant distribution is the joint beta distribution. This system of SDEs consists of N independent equations. For more on the beta SDE, see https:/
In addition to integrating the above SDE, there are two additional functions of are computed as
These equations compute the instantaneous mixture density, , and instantaneous specific volume, , for equation in the system. These quantities are used in binary mixing of variable-density turbulence between two fluids with constant densities, and . The additional parameters, and are user input parameters and kept constant during integration. Since we compute the above variables, and , and call them mixture density and specific volume, respectively, , governed by the beta SDE is a number (or mole) fraction, hence the name number-fraction beta.
All of this is unpublished, but will be linked in here once published.
- namespace walker
- Walker declarations and definitions.