Parabolic flows in which the pressure variation in the streamwise (or marching) direction is unknown a priori include internal thin shear layers, shock-boundary layer interactions, and inverse boundary layers with specified displacement thickness or shear stress. The pressure is typically obtained through an additional iteration beyond that required to determine the velocity components (and other dependent variables). A generalized block-tridiagonal procedure is discussed in which pressure is determined within the iteration for velocity components to substantially reduce computation time. The increase in algebraic complexity in the solution procedure is small; no increase in the size of the block matrices is required. The method applies to any marching solution in which a scalar dependent variable is constant across the flow, but varies in the streamwise or marching direction.

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