A dynamical pseudo-spectral domain decomposition technique: Application to viscous compressible flows
The authors present a dynamical spectral domain decomposition method based on transformation of coordinates that depends on one parameter in each subdomain. Both the mapping parametes and the location of interfaces are dynamically adapted by minimizing the norm of the calculated solution. Using the minimum norm that determines the best location of the interface, a dynamical generation of Chebyshev collocation points can be found. This method is applied to partial differential equations, and both the overall accuracy and the matching at the interfaces are improved with respect to a fixed interface calculation. Finally, the algorithm is used for numerical solution of the time-dependent compressible Navier-Stokes equations in two dimensions. Matching of the density is performed by a simple upwind procedure, whereas velocity, temperature and concentration are handled with the influence matrix method. Numerical examples include Kelvin-Helmholtz and Rayleigh-Taylor flows.
scientific article; zbMATH DE number 992120