Abstract
Treatment of the time-dependent Navier-Stokes equatipns for the solution of the flowfield about airfoil configurations is generally performed using either explicit or implicit finite-difference methods. As a viable alternative, hopscotch-type methods combine the speed of the explicit and the favorable stability criteria of the implicit methods. Such methods are constructed here for the time-dependent Navier-Stokes equations in conservation law form; their implementation to a number of test cases (one of Euler's equations), including the stringent case of shock-wave/bo undary-layer interaction with separation, indicates the possibility of competitive accuracy and more rapid computing time than is required by currently popular, fully implicit methods. , •' e = total enthalpy F,F',G,G' = defined in Eqs. (3) and (20), respectively ij = index / = identity matrix L = (nonlinear) finite-difference operator M = Mach number n = index P = pressure Pr = Prandtl number Q,Q',R,R' = defined in Eqs. (4) and (21), respectively Re = Reynolds number T - temperature T' = source term
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