The P-DNS method for turbulent fluid flows: An overview

Published in Archives of Computational Methods in Engineering, Vol. 31, pp. 973–1021, 2024
DOI: 10.1007/s11831-023-10004-3

Abstract

An overview of the Pseudo-Direct Numerical Simulation (P-DNS) method is presented. This is a multi-scale method aiming at numerically solving the unknown fields at two different scales, namely coarse and fine. The P-DNS method is built around four key ideas. The first one is that of numerically solving both scales, which facilitates obtaining solutions to problems of both concurrent multi-scale and hierarchical multi-scale types. The second key idea is that of computing off-line the fine solution via Direct Numerical Simulation in simplified domains, termed representative volume elements (RVEs), while the third idea is that of storing the basic (physics-informed) results obtained from this solution in a problem-independent unique dimensionless database. This database may be subsequently used for solving different problems at the coarse level, i.e. by using coarse meshes in the corresponding problem domains, via a surrogate model. In this sense P-DNS resembles Reduced Order Methods, which require a previous off-line evaluation of the modes to be used in the solution, sharing with them the benefit of solving the reduced problem, more precisely the coarse scale, in P-DNS terms, in a very efficient way. The fourth and last key idea of P-DNS is based on the fact that most of the high-frequency modes of a turbulent flow are convected by the fluid velocity of the low-frequency modes. Taking this into account the P-DNS technique is implemented in such a way that the fine instabilities are convected by the velocity field of the coarse solution. Finally, although the P-DNS method has been used to solve different computational mechanics problems, such as convection-diffusion and convection-reaction/absorption problems, the scope of this overview will be limited to its application to turbulent incompressible fluid flows, including both single phase and particle-laden flows.