Finite element methods of an operator splitting applied to population balance equations

Finite element methods of an operator splitting applied to population balance equations

In population balance equations, the distribution of the entities depends not only on space and time but also on their own properties referred to as internal coordinates. The operator splitting method is used to transform the whole time-dependent problem into two unsteady subproblems of a smaller complexity. The first subproblem is a timedependent convection-diffusion problem while the second o...

Operator Splitting Methods for Wave Equations

Abstract The motivation for our studies is coming from simulation of earthquakes, that are modelled by elastic wave equations. In our paper we focus on stiff phanomenons for the wave equations. In the course of this article we discuss iterative operator splitting methods for wave equations motivated by realistic problems dealing with seismic sources and waves. The operator splitting methods are...

Realizable high-order finite-volume schemes for quadrature-based moment methods applied to diffusion population balance equations

Dilute gas–particle flows can be described by a kinetic equation containing terms for spatial transport, gravity, fluid drag and particle–particle collisions. However, direct numerical solution of kinetic equations is often infeasible because of the large number of independent variables. An alternative is to reformulate the problem in terms of the moments of the velocity distribution. Recently,...

Additive Operator Splitting Methods for Solving Systems of Nonlinear Finite Difference Equations

There exists a considerably body of literature on the development, analysis and implementation of multiplicative and additive operator splitting methods for solving large and sparse systems of finite difference equations arising from the discretization of partial differential equations. In this note, we will review the Newton–Arithmetic Mean and the Modified Newton–Arithmetic Mean methods for s...

Higher-order operator splitting methods for deterministic parabolic equations