Energy stable boundary conditions for the nonlinear incompressible Navier-Stokes equations

Jan Nordström, Cristina La Cognata

Research output: Contribution to journalArticlepeer-review

22 Citations (Scopus)


The nonlinear incompressible Navier-Stokes equations with different types of boundary conditions at far fields and solid walls is considered. Two different formulations of boundary conditions are derived using the energy method. Both formulations are implemented in both strong and weak form and lead to an estimate of the velocity field. Equipped with energy bounding boundary conditions, the problem is approximated by using discrete derivative operators on summation-by-parts form and weak boundary and initial conditions. By mimicking the continuous analysis, the resulting semi-discrete as well as fully discrete scheme are shown to be provably stable, divergence free, and high-order accurate.

Original languageEnglish
Pages (from-to)665-690
Number of pages26
JournalMathematics of Computation
Issue number316
Publication statusPublished - 2019
Externally publishedYes


  • Boundary conditions
  • Divergence free
  • Energy estimate
  • High-order accuracy
  • Incompressible
  • Navier-Stokes equations
  • Stability
  • Summation-by-parts

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics


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