High-Order Entropy Stable Formulations for Computational Fluid Dynamics
نویسندگان
چکیده
A systematic approach is presented for developing entropy stable (SS) formulations of any order for the Navier-Stokes equations. These SS formulations discretely conserve mass, momentum, energy and satisfy a mathematical entropy inequality. They are valid for smooth as well as discontinuous flows provided sufficient dissipation is added at shocks and discontinuities. Entropy stable formulations exist for all diagonal norm, summation-by-parts (SBP) operators, including all centered finite-difference operators, Legendre collocation finite-element operators, and certain finite-volume operators. Examples are presented using various entropy stable formulations that demonstrate the current state-of-the-art of these schemes.
منابع مشابه
Computational fluid dynamics simulations for investigation of parameters affecting goaf gas distribution
It is necessary to obtain a fundamental understanding of the goaf gas flow patterns in longwall mine in order to develop optimum goaf gas drainage and spontaneous combustion (sponcom) management strategies. The best ventilation layout for a longwall underground mine should assist in goaf gas drainage and further reduce the risk of sponcom in the goaf. Further, in the longwall panel, regulators ...
متن کاملCFD Simulation of UV Disinfection Reactor for Applesauce with a Low UV Absorption Coefficient
In this study, a Computational Fluid Dynamics (CFD) model was developed to evaluate ultraviolet disinfection applesauce reactor. To simulate UV reactors, three sets of equations, including hydrodynamics, radiation and species mass conservation were solved simultaneously. The Realizable k-e turbulence model and the discrete ordinate method were used to find the UV radiation profile through the r...
متن کاملStabilized and Galerkin Least Squares Formulations
We study incompressible fluid flow problems with stabilized formulations. We introduce an iterative penalty approach to satisfying the divergence free constraint in the Streamline Upwind Petrov Galerkin (SUPG) and Galerkin Least Squares (GLS) formulations, and prove the stability of the formulation. Equal order interpolations for both velocities and pressure variables are utilized for solving p...
متن کاملEntropy Stable Approximations of Nonlinear Conservation Laws
A central problem in computational fluid dynamics is the development of the numerical approximations for nonlinear hyperbolic conservation laws and related time-dependent problems governed by additional dissipative and dispersive forcing terms. Entropy stability serves as an essential guideline in the design of new computationally reliable numerical schemes. My dissertation research involves a ...
متن کاملNumerical Simulation and Parametric Reduced Order Modeling of the Natural Convection of Water-Copper Nanofluid
In this article, a coupled computational framework is presented for the numerical simulation of mass transfer under the effects of natural convection phenomena in a field contains water-copper Nano-fluid. This CFD model is build up based on accurate algorithms for spatial derivatives and time integration. The spatial derivatives have been calculated using first order upwind and second order cen...
متن کامل