What is mathematical modelling and what is simulation?
Our group develops mathematical models of complex fluid flow involving chemical reactions, porous media, electromagnetic fields, radiative heat transfer, multiphase flow, to name a few. All these phenomena can be represented using physical and chemical laws through sets of strongly coupled sets of equations. These may be non-linear partial differential equations, integro-differential equations, difference equations, etc... that must be transformed and combined. Some of the tools that are used to solve these complex coupled systems of equations come from the rich field of the Computational Fluid Dynamics (CFD), and the solution using these tools is often named numerical simulation. In essence, the mathematical model is based on the physico-chemical laws governing the system while the numerical simulation involves the selection of the appropriate numerical techniques and the optimisation of the computational techniques used.