Direct Numerical Simulation in CFD via Lagranian Formulations and Multi-Scale Homogenization

IDELSOHN, SERGIO; NIGRO NORBERTO; LARRETEGUY AXEL; GIMENEZ JUAN; RYZHAKOV PAVEL

Boulder

Conferencia; Quantification of Coupled Physics Problems; 2018

Although the Navier-Stokes equations are equivalently applicable to both laminar andturbulent fluid flows, the current computing power generally precludes employing finemeshes that would allow to simulate turbulent flows without introducing empiricalapproximations. The prediction power of the models is therefore restricted to problems withinthe margins of the selected empirical approximation. Solving a problem without suchapproximations on a mesh sufficiently fine so as to represent the whole expected range ofeddy sizes is known as ?Direct Numerical Simulation? (DNS). Taking into account that amany fluid flow problems of industrial interest are indeed turbulent, it is worthwhile tocontinue improving the models so that they fit more and more with the physics of theproblem.Simulating a CFD problem in a given domain with a ?fine enough? DNS meshintroduces an unmanageable number of unknowns for current computers. The project we areworking on involves modelling turbulent flow in a DNS fashion, i.e. without any additionalturbulence model. However, we strive to develop an approach considerably morecomputationally efficient than a classical DNS.The basic idea is as follows. The global (macro) domain, can be subdivided into manyequally-shaped small domains, the so-called RVEs, ?Representative Volume Elements?(micro problems). These RVEs, in principle, can be solved individually and independentlyfrom each other. The RVEs may even be previously solved off-line for different time-dependant loads. The micro and macro problems require to be coupled. This will beperformed via the theory known as ?homogenization?.Another important aspect of the solution process in our approach is the use of aLagrangian fluid formulation at the macro level [1]. The Lagrangian particles will take carenot only of the transport of the macro-velocity, but also of the micro-eddies that may appearin some RVEs, thus convecting the turbulent energy. This is a very important feature inturbulent flows where turbulence is produced in some high gradient regions and is thenconvected and diffused to other regions with different gradients.Finally, concerning the off-line solution of the RVEs for different time-dependingloads, a Reduction Order Model (ROM) [2], a Machine Learning technique or a pseudo-spectral (FFT + Chebychev) will be tested in order to obtain a sensible speed-up.This presentation is a work in progress, aimed more at opening a discussion on thetopic, rather than presenting elaborate results.