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Brief facts about 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 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.

Finite volume method - The finite volume method is a method for representing and evaluating partial differential equations in the form of algebraic equations LeVeque, 2002; Toro, 1999 .

Flux limiter - Flux limiters are used in high resolution schemes – numerical schemes used to solve problems in science and engineering, particularly fluid dynamics, described by partial differential equations.

Godunov's theorem - In numerical analysis and computational fluid dynamics, Godunov's theorem — also known as Godunov's order barrier theorem — is a mathematical theorem important in the development of the theory of high resolution schemes for the numerical solution of partial differential equations.

High resolution scheme - High-resolution schemes are used in the numerical solution of partial differential equations where high accuracy is required in the presence of shocks or discontinuities. They have the following properties...

Numerical method of lines - The method of lines is a technique for solving partial differential equations in which all but one dimension is discretized. MOL allows standard, general-purpose methods and software, developed for the numerical integration of ODEs and DAEs, to be used.

Sergei K. Godunov - Sergei Konstantinovich Godunov is professor at the Sobolev Institute of Mathematics of the Russian Academy of Sciences in Novosibirsk, Russia.

Computational fluid dynamics

Numerical differential equations