CONVERGENCE STUDY OF AN IMPLICIT MULTIDOMAIN APPROXIMATION FOR THE COMPRESSIBLE EULER EQUATIONS

The influence of grid overlapping on the convergence to a steady state is studied for a time-dependent multidomain difference approximation of a hyperbolic initial boundary value problem. Implicit dissipative d ifference schemes for interior points and explicit matching conditions at grid interfaces are considered. For a scalar model equation, it is proved that when the total number of interior mesh points is large, t he convergence speed is an increasing function of the overlapping leng th. The convergence rate of the corresponding single domain treatment is recovered for a sufficiently large overlapping length. For a partic ular scheme, a quantitative analysis shows the existence of an optimal overlapping length, equal to the CFL number, for which the multidomai n scheme converges as well as and sometimes even better than the singl e domain one in terms of the CPU time. Numerical experiments on a quas i-one-dimensional supersonic flow in a duct show also that a proper ch oice of the overlapping length ensures the same convergence rate as th e one in the single domain calculation. Further applications to transo nic flow calculations over single and two-element airfoils reveal the good convergence property of the overlapping treatment even for proble ms containing shocks.