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.

Features

The Advection Upstream Splitting Method has many features. The main features are:

• accurate capturing of shock and contact discontinuities
• entropy-satisfying solution
• positivity-preserving solution
• algorithmic simplicity (not requiring explicit eigen-structure of the flux Jacobian matrices) and straightforward extension to additional conservation laws
• free of “carbuncle” phenomena
• uniform accuracy and convergence rate for all Mach numbers.

Since the method does not specifically require eigenvectors, it is especially attractive for the system whose eigen-structure is not known explicitly, as the case of two-fluid equations for multiphase flow.

Applications

The AUSM has been employed to solve a wide range of problems, low-Mach to hypersonic

Hypersonic

In aerodynamics, a hypersonic speed is one that is highly supersonic. Since the 1970s, the term has generally been assumed to refer to speeds of Mach 5 and above...

 aerodynamics

Aerodynamics

Aerodynamics is a branch of dynamics concerned with studying the motion of air, particularly when it interacts with a moving object. Aerodynamics is a subfield of fluid dynamics and gas dynamics, with much theory shared between them. Aerodynamics is often used synonymously with gas dynamics, with...

, large eddy simulation and aero-acoustics, direct numerical simulation, multiphase flow, galactic relativistic flow etc.

See also

• Euler equations
  Euler equations
  In fluid dynamics, the Euler equations are a set of equations governing inviscid flow. They are named after Leonhard Euler. The equations represent conservation of mass , momentum, and energy, corresponding to the Navier–Stokes equations with zero viscosity and heat conduction terms. Historically,...
  
  
• Finite volume method
  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 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
  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.The theorem states...
  
  
• High resolution scheme
  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...
  
  
• Numerical method of lines
  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 K. Godunov
  Sergei Konstantinovich Godunov is professor at the Sobolev Institute of Mathematics of the Russian Academy of Sciences in Novosibirsk, Russia....
  
  
• Total variation diminishing
  Total variation diminishing
  In numerical methods, total variation diminishing is a property of certain discretization schemes used to solve hyperbolic partial differential equations...