Multiscale Simulations of Heat Transfer and Fluid Flow Problems

Abstract

Multiscale simulation is a rapidly evolving area of research that will have a great impact on computational mathematics and numerical modeling in engineering. In this keynote lecture following parts are included. First, what is multiscale problem. In the thermal and fluid science multiscale problems may be classified into two categories: multiscale process and multiscale system. By multiscale process we mean that the overall behavior is governed by processes occur at different length scales. By multiscale system we refer to a system that is characterized by a large variation in length scales. The cooling of an electronic system is such a typical multiscale system. Existing numerical methods for three geometric scales (macro, meso and micro) are briefly mentioned. In the second part the necessity of multiscale simulation is discussed. Examples are provided for multiscale process and multiscale system. In this lecture focus is put on the simulation of multiscale process. In the third section numerical approaches developed for the simulation of multiscale processes are presented. There are two types of simulation approaches. One is the usage of a general governing equation and solving the entire flow field involving a variation of several orders in characteristic geometric scale. The other is the so-called “solving regionally and coupling at the interfaces”. In this approach the processes at different length level is simulated by different numerical methods and then information is exchanged at the interfaces between different regions. The exchange of information should be conducted in a way that is physically meaningful, mathematically stable, and computationally efficient. The key point is the establishment of the reconstruction operator, which transforms the data of few variables of macroscopic computation to large amount of variables of microscale or mesoscale simulation. For different coupling cases the existing methods for such operators are briefly reviewed. In the fourth part, four numerical examples of multiscale simulation are presented: liquid flow in nanochannels with roughness by using MDS and FVM, flow and heat transfer in a micro nozzle by using DSMC in fluid and FVM in solid, flow past a cylinder and natural convection heat transfer in a square cavity by using coupled FVM and LBM. Finally, it is pointed out that we have a long way to go in order to have a successful full multiscale simulation for the complicated engineering problems as transport process in PEMFC and refrigerant condensation process on a enhanced surface. Further researches are highly required to establish robust and quick-convergent numerical solution approaches. Some further research needs are proposed.