Construction of interface conditions for solving the compressible Euler equations by non-overlapping domain decomposition methods

In this work we examine the acceleration of the convergence of a non-overlapping additive Schwarz-type algorithm by modifying the transmission conditions applied to the subdomain interfaces. We have built generalized zero-order interface conditions using the Smith theory of diagonalizing polynomial matrices. The numerical experiments confirmed qualitatively the behaviour in accordance with the theory, but we could not reproduce identically the results obtained in the continuous case. The preliminary results are very encouraging since they lead to a very good convergence rate for certain Mach numbers.