A Quasi-simultaneous Finite Difference Approach for Strongly Interacting Flow
Viscous effects can have a substantial impact on the aerodynamic performance of internal and external flow configurations. For a significant number of flows of practical interest, the Reynolds number is sufficiently large for the flow field to be represented by interacting boundary layer theory (IBLT), whereby the flow is divided into viscous and in viscid flow regions with the two regions coupled through the viscous displacement thickness. The formal justification for the use of IBLT in the prediction of high Reynolds number strong interaction laminar flows is provided by triple deck theory , which is obtained from an asymptotic expansion of the Navier—Stokes equations. In IBLT the viscous region is represented by the Prandtl boundary layer equations; the inviscid flow can be represented in a number of different ways which depend on the flow configuration and the Mach number. It is clear from previous work (see  for a review) that many flows with separation can be solved accurately (neglecting the problems of modeling the turbulence and transition processes) through the use of IBLT. A critical step in the numerical solution of the governing equations in IBLT is the coupling mechanism which connects the viscous and inviscid flow equations. Several coupling algorithms currently exist for strongly interacting flows; however, the efficiency of these procedures, which are discussed below, generally decreases, along with the possibility of unstable behavior, as the size of the separation region increases.
KeywordsSeparation Bubble Separate Flow Boundary Layer Equation Inviscid Flow Displacement Thickness
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