A Posteriori Modeling Error Estimates for the Assumption of Perfect Incompressibility in the Navier-Stokes Equation

@article{Fischer2015APM,
  title={A Posteriori Modeling Error Estimates for the Assumption of Perfect Incompressibility in the Navier-Stokes Equation},
  author={Julian Fischer},
  journal={SIAM J. Numerical Analysis},
  year={2015},
  volume={53},
  pages={2178-2205}
}
We derive a posteriori estimates for the modeling error caused by the assumption of perfect incompressibility in the incompressible NavierStokes equation: Real fluids are never perfectly incompressible, but always feature at least some low amount of compressibility. Thus, their behavior is described by the compressible Navier-Stokes equation, the pressure being a steep function of the density. We rigorously estimate the difference between an approximate solution to the incompressible Navier… CONTINUE READING

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