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

• We introduce an interface/coupling procedure for hyperbolic problems posedon 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.

Subject headings

NATURVETENSKAP  -- Matematik -- Beräkningsmatematik (hsv//swe)

NATURAL SCIENCES  -- Mathematics -- Computational Mathematics (hsv//eng)

Keyword

Finite difference

High order accuracy

Deforming domains

Time-dependent interface

Well-posedness

Conservation

Summation-by-parts

Stability

Hyperbolic problems

Publication and Content Type

vet (subject category)

rap (subject category)