In this chapter, some real-life model problems that can be formulated as ordinary differential equations (ODEs) are introduced and numerically studied. These models are the variable-order fractional Hodgkin–Huxley model of neuronal excitation (VOFHHM) and other models with the variable-order fractional (VOF) time delay, such as the 4year life cycle of a population of lemmings model, the enzyme ...

We study microreactors with internal fields of posts as typical examples of structured microreactors to elucidate flow fields and their implications for mass transfer. Laser-induced fluorescence (LIF) visualization combined with image analysis is used to systematically quantify key features such as interfacial area, phase holdup and the characteristics of the post-wetting layer. The subsequent ...

The paper describes a novel implementation of the piecewise linear interface-capturing volume-of-fluid method (PLIC-VOF) in axisymmetric cylindrical coordinates. principal innovative feature involved this work is that both forward and inverse reconstruction problems are solved analytically, resulting an appreciable speed-up computing time comparison with iterative approach. All formulae introdu...

In this study, an efficient conversion algorithm of level set function ϕ from volume fraction α is developed. This method makes the calculation easier than conventional CLSVOF method, and precision surface tension can be improved by application ϕ. The two numerical tests are shown to demonstrate proposed scheme. As a result demonstration tests, it obtained that (a) gives better existing simple ...