Dimension reduction method for ODE fluid models

We develop a new dimension reduction method for large size ODE systems obtained from a discretization of partial differential equations of viscous single and multiphase fluid flow. The method is also applicable to other large size classical particle systems with negligibly small variations of particle concentration. We propose a new computational closure for mesoscale balance equations based on numerical iterative deconvolution. To illustrate the computational advantages of the proposed reduction method, we use it to solve a system of Smoothed Particle Hydrodynamic ODEs describing single phase and two-phase layered Poiseuille flows driven by uniform and periodic (in space) body forces. For the single phase Poiseuille flow driven by the uniform force, the coarse solution was obtained with the zero-order deconvolution. For the single phase flow driven by the periodic body force and for the two-phase flows , the higher-order (the firstand second-order ) deconvolutions were necessary to obtain a sufficiently accurate solution.