An integral equation of the transonic small-disturbance differential equation is extended to second order for supersonic flows around three-dimensional thin wings, allowing bow as well as embedded shock waves. An explicit solution of the second-order small-disturbance equations satisfying the second-order boundary conditions of a wing is obtained. The particular solution is expressed as the differentiation of a volume integral with specifically chosen boundaries, and the complementary solution satisfies the linearized velocity potential equation with appro- priate boundary conditions.
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