Entropy Stable Approximations of Navier-Stokes Equations With No Artificial Numerical Viscosity

Abstract

We construct a new family of entropy stable difference schemes which retain the precise entropy decay of the Navier-Stokes equations, d/dt Integral(sub x) of (-p S)dx = - Integral(sub x)((Lambda + 2Mu)q(sub x)squared /Theta = Kappa (Theta(sub x)/Theta)squared) dx. To this end we employ the entropy conservation differences of [Tadmor2004] to discretize Euler convective fluxes, and centered differences to discretize the dissipative fluxes of viscosity and heat conduction. The resulting differences schemes contain no artificial numerical viscosity in the sense that their entropy dissipation is dictated solely by viscous and heat fluxes. Numerical experiments provide a remarkable evidence for the different roles of viscosity and heat conduction in forming sharp monotone profiles in the immediate neighborhoods of shocks and contacts.

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Document Details

Document Type
Technical Report
Publication Date
Dec 10, 2005
Accession Number
ADA448262

Entities

People

  • Eitan Tadmor
  • Weigang Zhong

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Energy and Power Technologies

DTIC Thesaurus Topics

  • Boltzmann Equation
  • Computational Fluid Dynamics
  • Computations
  • Differential Equations
  • Discontinuities
  • Equations
  • Euler Equations
  • Fluid Dynamics
  • Heat Energy
  • Heat Flux
  • Mathematical Analysis
  • Mathematics
  • Mechanical Properties
  • Navier Stokes Equations
  • Thermal Conductivity
  • Universities
  • Viscosity

Fields of Study

  • Mathematics

Readers

  • Analytical Mechanics
  • Computational Fluid Dynamics (CFD)
  • Statistical inference.