A Physical Insight into Computational Fluid Dynamics and Heat Transfer

Mathematical equations that describe all physical processes are valid only under certain assumptions. One of them is the minimum scales used for the given description. In fact, this prohibits the use of derivatives in the mathematical models of the physical processes. This article represents a derivative-free approach for the mathematical modelling. The proposed approach for CFD and numerical heat transfer is based on the conservation and phenomenological laws, and physical constraints on the minimum problem-dependent spatial and temporal scales (for example, on the average free path of molecules and the average time of their collisions for gases). This leads to the derivative-free governing equations (the discontinuum approximation) that are very convenient for numerical simulation. The theoretical analysis of governing equations describing the fundamental conservation laws in the continuum and discontinuum approximations is given. The article demonstrates the derivative-free approach based on the correctly defined macroparameters (pressure, temperature, density, etc.) for the mathematical description of physical and chemical processes. This eliminates the finite-difference, finite-volume, finite-element or other approximations of the governing equations from the computational algorithms.