Skip to main content
NASA Advanced Supercomputing (NAS) Division World-class modeling, simulation, and supercomputing in support of the NASA mission

Navier-Stokes Equations: Reliability, UQ, and Extension for Strong Nonequilibrium Flows

AMS Seminar Series

Speaker: Narendra Singh, Stanford University

Presentation

Seminar Slide Deck (PDF-14MB)

Abstract

In this talk, starting from kinetic theory, I will present the development of a rigorous metric to assess the breakdown of the Navier-Stokes equations. The Navier-Stokes equations have been fundamental to understanding continuum fluid mechanics for a range of complex problems in nature. While thermodynamic fluxes such as stresses and heat flux vector in these equations are based on linear irreversible thermodynamics, the equations are widely used for gas flows under strong nonequilibrium. Multiscale problems such as hypersonic flows with strong nonequilibrium due to strong shocks, and expansions result in flow physics which is no longer accurately described by the Navier-Stokes equations. Similarly, the Navier-Stokes equations breakdown in rarefied (low density) gas flows. Therefore, hybrid methods, which can combine continuum description using the Navier-Stokes equations and microscopic description, are necessary for efficient high-fidelity numerical simulations. A key input to hybrid methods is a metric to identify regions in the flow-field where the Navier-Stokes equations break down for switching to a microscopic description. In addition to proposing a metric, we quantify the uncertainty due to nonequilibrium physics modeling in transport relations without apriori knowledge of the accurate solutions. The metric and the mathematical framework are directly relevant to high-speed simulations, which are important for emerging interest in space missions and hypersonic flights. Other wide range of physics problems such as nano-scale flows, plasma physics modeling, and general complex gas flows can benefit immensely from the proposed formalism.

Biography

Photo of Narendra Singh
Narendra Singh graduated with a Ph.D. (and MS) in Aerospace Engineering (with a minor in Mathematics and Chemistry) from University of Minnesota. He obtained his undergraduate degree (with Honors) in Mechanical Engineering from IIT Bombay. In his doctoral thesis, Narendra developed chemical kinetics models for DSMC and CFD using a first principles-based approach for hypersonic flows. He (along with Prof. Agrawal) has developed higher order equations for rarefied and strong nonequilbrium flows, known as O-13 and O-Burnett equations, where O ‘refers’ to Onsager due to the consistency of equations with Onsager’s reciprocity principle. Currently, Narendra Singh is a postdoc in MechE at Stanford, where his research spans particle-laden flows, carbon sequestration, and ultrafast chemistry at SLAC.