Engineering Applications

Abstract

In this chapter, we discuss the different engineering applications related to multicomponent and multiscale models, that occur in different categories (microscopic, mesoscopic and macroscopic). As we have described in the Introduction on p. xxv. That such models can be used as basic model to couple to more complicate models, describing materials, interfaces, etc., see Rosso and de Baas (Review of materials modelling: what makes a material function? Let me compute the ways, 2014, [1]).We deal with the following engineering applications with the two classified multiscaling approaches, see also the Introduction on p. xxv and in Fig. 5.1:• Different time-or spatial scales of same model (mono model or basic model).• Linking of different models (different models or multimodel).One of the main contributions to link the different scales and models together are the coupling techniques. In our motivation, such coupling of different time-and spatial scales or coupling of different models, need the suggested methods, e.g. multiscale methods, multicomponent methods, that allow a data transfer between the different scales and models. Such methods, we have introduced in the previous sections and now, we will close the gap between the theoretical discussions of methods and their applications to engineering problems. In such a stage, we have to adapt the numerical schemes with respect to the real-life properties and we obtain truly working multiscale approaches, that we solve the engineering complexities, see [1].Based on the real-life applications, we could study such helpful coupling of different scales or different models. Therefore, we overcome the gap of the recent problem in linking different scales of complicated engineering models in the industrial applications. Multiscale Methods for Langevin-Like EquationsAbstract In this section, we discuss multiscale methods, that solve Langevin-like equations, see [2]. The underlying ideas are to split into a deterministic and stochastic part of the Langevin equation, see [3]. The splitting methods are based on additive and iterative schemes, which are discussed with respect of their benefits and drawbacks, see [4]. We are motivated to reduce computational time for Coulomb collisions in plasma done in particle simulations. We extend splitting schemes, which are well-known in deterministic applications, to stochastic applications and modify the methods with respect to the stochastic terms. Such an idea allows to solve the multiscale behaviour of the coarse deterministic and fine stochastic timescales in an adequate computational time. Introduction of the ProblemIn the underlying problem, we are motivated to develop fast algorithms to solve the Coulomb collisions in plasma simulations, see [5].Recently in the literature, we can find two main ideas to deal with the Coulomb collisions in particle simulations. Here we have the following two ideas:• Binary algorithm: Particles in a finite cell selected into binary pairs. The collision is computed by the scattered velocities by an ...