Impact of computational physics on multi-scale CFD and related numerical algorithms

Development of accurate computational methods for the constitutive relation that plays a role as the bridge between microscopic and macroscopic physics becomes a key issue in a continuum approach for describing rarefied and micro-scale gas flows. The mathematical form of the constitutive relation dictates the resulting computational methods and related algorithms. It is, therefore, vital to develop proper computational models on the basis of a correct understanding of the multi-scale physics inherent in non-equilibrium gases. In this study the computational issue is discussed by considering two benchmark multi-scale problems: the compression-dominated shock structure and velocity shear-dominated gas flows. Special emphasis is placed on efficient CFD algorithms within the finite volume formulation. In addition, the verification and validation issue of the multi-scale methods is discussed and a simple verification method based on basic physical laws is proposed.