PNNL

Abstract

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