An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations

Fatemeh Ghasemi, Jan Nordström

Research output: Contribution to journalArticlepeer-review


The coupling of the compressible and incompressible Navier-Stokes equations is considered. Our ambition is to take a first step towards a provably well posed and stable coupling procedure. We study a simplified setting with a stationary planar interface and small disturbances from a steady background flow with zero velocity normal to the interface. The simplified setting motivates the use of the linearized equations, and we derive interface conditions such that the continuous problem satisfy an energy estimate. The interface conditions can be imposed both strongly and weakly. It is shown that the weak and strong interface imposition produce similar continuous energy estimates. We discretize the problem in time and space by employing finite difference operators that satisfy a summation-by-parts rule. The interface and initial conditions are imposed weakly using a penalty formulation. It is shown that the results obtained for the weak interface conditions in the continuous case, lead directly to stability of the fully discrete problem.

Original languageEnglish
Pages (from-to)280-302
Number of pages23
JournalJournal of Computational Physics
Publication statusPublished - 1 Nov 2019
Externally publishedYes


  • Compressible fluid
  • Energy estimate
  • Incompressible fluid
  • Interface conditions
  • Navier-Stokes equations
  • Stability

ASJC Scopus subject areas

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • General Physics and Astronomy
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics


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