Special Seminar in Applied Computational Mathematics
During the last decade, provably stable high order methods for initial-boundary-value-problems have been developed. The stability is due to the use of so-called Summation-By-Parts (SBP) operators , penalty techniques for implementing boundary and interface conditions using Simultaneous Approximation Terms (SAT), and the energy method for proving stability.
In this talk we will present SBP-SAT technique and relate it to the approximated initial-boundary-value-problem.
In particular we will discuss the coupling of incompressible and compressible Navier-Stokes equations, encapsulation techniques for difference operators on curvilinear grids, inflow boundary conditions for internal flow calculations and multigrid methods for hyperbolic problems.
Applications can be found in aeronautics, weather prediction, oceanography and all kinds of problems involving signal and sound propagation.