Prandtl–Glauert transformation

The Prandtl–Glauert transformation is a mathematical technique which allows solving certain compressible flow problems by incompressible-flow calculation methods. It also allows applying incompressible-flow data to compressible-flow cases.

Inviscid compressible flow over slender bodies is governed by linearized compressible small-disturbance potential equation:

${\displaystyle \phi _{xx}\,+\,\phi _{yy}\,+\,\phi _{zz}\;=\;M_{\infty }^{2}\phi _{xx}\;\;\;\;{\mbox{(in flowfield)}}}$

together with the small-disturbance flow-tangency boundary condition.

${\displaystyle V_{\infty }\,n_{x}\,+\,\phi _{y}\,n_{y}\,+\,\phi _{z}\,n_{z}\;=\;0\;\;\;\;{\mbox{(on body surface)}}}$

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