A fully discrete, stable and conservative summation-by-parts formulation for deforming interfaces

Samira Nikkar, Jan Nordström

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


We introduce an interface/coupling procedure for hyperbolic problems posed on time-dependent curved multi-domains. First, we transform the problem from Cartesian to boundary-conforming curvilinear coordinates and apply the energy method to derive well-posed and conservative interface conditions. Next, we discretize the problem in space and time by employing finite difference operators that satisfy a summation-by-parts rule. The interface condition is imposed weakly using a penalty formulation. We show how to formulate the penalty operators such that the coupling procedure is automatically adjusted to the movements and deformations of the interface, while both stability and conservation conditions are respected. The developed techniques are illustrated by performing numerical experiments on the linearized Euler equations and the Maxwell equations. The results corroborate the stability and accuracy of the fully discrete approximations.

Original languageEnglish
Pages (from-to)500-524
Number of pages25
JournalJournal of Computational Physics
Publication statusPublished - 15 Jun 2017
Externally publishedYes


  • Conservation
  • Deforming domains
  • Finite difference
  • High order accuracy
  • Hyperbolic problems
  • Stability
  • Summation-by-parts
  • Time-dependent interface
  • Well-posedness

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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