3-DIMENSIONAL MIXED EXPLICIT-IMPLICIT GENERALIZED GALERKIN SPECTRAL ELEMENT METHODS FOR HIGH-SPEED TURBULENT COMPRESSIBLE HOWS

In high speed flows the interactions of shock waves with turbulent bou ndary layers are important design considerations because of the comple x flowfields resulting in increased adverse pressure gradients, skin f riction and temperatures. Unsteadiness and three-dimensional flowfield structure are also characteristic of shock wave turbulent boundary la yer interactions. Such physical phenomena require sophisticated numeri cal schemes in the solution of governing equations. The purpose of thi s paper, therefore, is to introduce an accurate and efficient approach -the Mixed Explicit-Implicit Generalized Galerkin Spectral Element Met hod (MEI-GG-SEM) with Legendre polynomial spectral elements in which f lowfield dependent implicitness parameters provide automatically adequ ate computational requirements for compressible and incompressible how s or high speed and low speed flows. This is in contrast to the tradit ional approach in which all-speed-regime analysis requires a separate hyperbolic-elliptic pressure equation for pressure correction if the f low becomes incompressible. In the MEI-GG-SEM scheme, mesh refinements are carried out adaptively until shock waves are resolved, followed t hen by the adaptive increase of Legendre polynomial degrees until turb ulence microscales are resolved, in which the traditional turbulence m odeling is no longer required, aimed toward direct numerical simulatio n. In order to demonstrate the validity of the theory and numerical pr ocedure, two-dimensional flat plate and compression corner high speed flows are investigated, followed by a three-dimensional sharp leading edged fin for swept shock wave turbulent boundary layer interactions. Comparisons of the present study with experimental measurements and ot her numerical studies show favorable agreement.