The numerical speed of sound is a variable that is used in the numerical solution of flows from low to high speeds. The numerical speed of sound is an effective speed of sound associated with Mach numbers used in the numerical splitting of a flow into upwind and downwind mass-flux components that are defined on the faces of cells of a computational grid into which a flow volume is divided. Depending on the details of a given flow problem and the algorithm chosen to solve it, the numerical speed of sound may or may not equal the physical speed of sound.

Pressure Contours on a Wing were computed by using a scheme called 'AUSM+,' augmented with the numerical speed of sound, to solve the Navier-Stokes equations numerically. The wing is of the M6 type of the Office National d'Etudes et de Recherches Aérospatiales (ONERA). The flow conditions for this computation were a free-stream speed of mach 0.84, a Reynolds number of 18.2×10^6, and an angle of attack of 3°. The computed pressure contours are in good agreement with available experimental data, especially in capturing two shocks that manifest themselves in the l-shaped pattern of closely spaced curves.

The numerical speed of sound has been found to be very useful in constructing upwind numerical-solution schemes to satisfy certain criteria. [As used in this special context, "upwind" (as distinguished from "central" or "downwind") refers to a manner of approximating spatial derivatives of flow quantities by taking differences between discretized flow quantities at locations biased toward the upwind side with respect the location of immediate interest.] An especially notable criterion is the capability for exact capturing of contact and shock discontinuities in one-dimensional flows. The concept of the numerical speed of sound can also be extended to apply to the computation of low-speed (in effect, incompressible) flows. In such an application, a scaling factor that varies with speed is introduced. As a result, the numerical dissipation decreases with the flow speed and, as a further consequence, the rate of convergence of iterative computations toward the solution is increased. The accuracy of the solution is also increased.

In a study, the numerical speed of sound was incorporated into some numerical-solution schemes based on a method called advection-upstream-splitting method (AUSM). It can also be incorporated in other upwind schemes, including one known as Roe flux splitting, wherein an averaged speed of sound, among several other averaged variables, is automatically required. Other numerical-solution schemes can also be made to capture shocks exactly.

This work was done by Meng-Sing Liou of Glenn Research Center and Jack R. Edwards of North Carolina State University. For further information, access the Technical Support Package (TSP) free on-line at  under the Information Sciences category.

Inquiries concerning rights for the commercial use of this invention should be addressed to

NASA Glenn Research Center
Commercial Technology Office
Attn: Steve Fedor
Mail Stop 4 —8
21000 Brookpark Road
Ohio 44135.

Refer to LEW-17011.