A rectangular-coordinate method for calculating nonlinear transonic potential flowfields in compressor cascades

Review—Computational Methods for Internal Flows With Emphasis on Turbomachinery

“…The resultant system of algebraic equations is solved by standard techniques. This approach was applied in the early work of Dodge [17], Ives [18,19], and Rae [20]. More recently this method has been used by Caspar [21,22], who applies it to discrete areas throughout the physical domain.…”

“…The first, and most common, is successive line over relaxation (SLOR). This is employed by Farrell [26], Dulikravich [24,25], Ives [18,19], Fruhauf [27], Rae [20], and Hirsch [32]. Other approaches employ a direct solver, typically Gaussian [32] elimination, as the noniterative part of an overall solution scheme.…”

“…This has the effect of introducing an artificial viscosity to the solution procedure, which assures its stability in supersonic regions. This artificial viscosity approach is employed principally by investigators using the nonconservation form of the full potential equation, Dulikravich [24], Ives [18], Rae [20], and Fruhauf [27]. Dodge [17], who also solves the nonconservation form, constructs hyperbolic and elliptic operators on a near-characteristic grid, updated during the course of calculation.…”

Theoretical Studies of Three Dimensional Transonic Flow through a Compressor Blade Row.

“…ASME Gas Turbine Conference, London, England, April 9-13, 1978.2. NASA Lewis Research Center, Workshop on Computational Fluid DynamicsApplied to Turbomachinery; Cleveland, OH, November[14][15] 1978. 3.…”