A Quasi-Simultaneous Interactive Boundary-Layer Model for a Cartesian Euler Solver

An interactive boundary-layer method has been implemented within a Cartesian-meshbased Euler solver, Cart3D. Although Euler-boundary layer solvers have not been in common use since the 1990s, they have a significant speed advantage over Navier-Stokes codes, particularly when the inviscid solver uses a Cartesian grid with automated meshing capabilities. Another advantage of Euler-boundary layer solvers is the capability to predict detailed boundary-layer properties such as those required for transition prediction. Due to the needs of design and optimization, robustness and speed are major concerns. It has been found that considerable care and attention to the mathematics of coupled equations is necessary in order to achieve fast and robust interactive viscous-inviscid solutions with a Cartesian-meshbased inviscid solver. Three coupling methods, direct, semi-inverse, and quasi-simultaneous have been evaluated. Each is described, and both advantages and disadvantages are discussed. The quasi-simultaneous coupling method is chosen as the overall best algorithm for the present implementation and a version is described that is valid from subsonic to supersonic flow regimes.

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