The direct quadrature method of moments fully conservative
In this appendix we discuss the problem of moment conservation with the DQMOM, and present a variation called DQMOM fully conservative (DQMOM-FC) that can be employed to partially overcome it. To illustrate the issue, we consider a one-dimensional spatially inhomogeneous PBE for the univariate NDF n(t, x, ξ) with constant velocity and constant diffusion coefficient as described in Section 8.3. However, as will become clearer below, the extension to other, more complex, problems is straightforward.
D.1 Inhomogeneous PBE
Let us consider the simple spatially inhomogeneous PBE:
where the particle velocity u and diffusion coefficient Γ are constant (i.e. they do ...