Abstract
The relevance of nonequilibrium phenomena, nonlinear behavior, gravitational effects and fluid compressibility in a wide range of problems related to hightemperature gasdynamics, especially in thermal, mechanical and nuclear engineering, calls for a concerted approach using the tools of the kinetic theory of gases, statistical physics, quantum mechanics, thermodynamics and mathematical modeling in synergy with advanced numerical strategies for the solution of the NavierStokes equations. The reason behind such a need is that in many instances of relevance in this field one witnesses a departure from canonical models and the resulting inadequacy of standard CFD approaches, especially those traditionally used to deal with thermal (buoyancy) convection problems. Starting from microscopic considerations and typical concepts of molecular dynamics, passing through the Boltzmann equation and its known solutions, we show how it is possible to remove past assumptions and elaborate an algorithm capable of targeting the broadest range of applications. Moving beyond the Boussinesq approximation, the Sutherland law and the principle of energy equipartition, the resulting method allows most of the fluid properties (density, viscosity, thermal conductivity, heat capacity and diffusivity, etc.) to be derived in a rational and natural way while keeping empirical contamination to the minimum. Special attention is deserved as well to the wellknown pressure issue. With the application of the socalled multiple pressure variables concept and a projectionlike numerical approach, difficulties with such a term in the momentum equation are circumvented by allowing the hydrodynamic pressure to decouple from its thermodynamic counterpart. The final result is a flexible and modular framework that on the one hand is able to account for all the molecule (translational, rotational and vibrational) degrees of freedom and their effective excitation, and on the other hand can guarantee adequate interplay between molecular and macroscopiclevel entities and processes. Performances are demonstrated by computing some incompressible and compressible benchmark test cases for thermal (gravitational) convection, which are then extended to the hightemperature regime taking advantage of the newly developed features.
Original language  English 

Pages (fromto)  687712 
Number of pages  26 
Journal  Journal of Computational Physics 
Volume  313 
Early online date  27 Feb 2016 
DOIs  
Publication status  Published  15 May 2016 
Keywords
 buoyancy convection
 high temperature
 projection method
 nonBoussinesq effects
 molecular degree of freedom excitation
Fingerprint Dive into the research topics of 'A mathematical and numerical framework for the analysis of compressible thermal convection in gases at very high temperatures'. Together they form a unique fingerprint.
Profiles

Marcello Lappa
Person: Academic