##### Wikipedia

### AUSM

**AUSM** stands for Advection Upstream Splitting Method. It is developed as a numerical inviscid flux function for solving a general system of conservation equations. It is based on the upwind concept and was motivated to provide an alternative approach to other upwind methods, such as the Godunov method, flux difference splitting methods by Roe, and Solomon and Osher, flux vector splitting methods by Van Leer, and Steger and Warming. The AUSM first recognizes that the inviscid flux consist of two physically distinct parts, i.e., convective and pressure fluxes. The former is associated with the flow (advection) speed, while the latter with the acoustic speed; or respectively classified as the linear and nonlinear fields. Currently, the convective and pressure fluxes are formulated using the eigenvalues of the flux Jacobian matrices. The method was originally proposed by Liou and Steffen for the typical compressible aerodynamic flows, and later substantially improved in to yield a more accurate and robust version. To extend its capabilities, it has been further developed in for all speed-regimes and multiphase flow. Its variants have also been proposed.