The advection upstream splitting method (AUSM) is developed as a numerical

inviscid The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the inte ...

flux Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications to physics. For transport ph ...

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 In the field of physics, engineering, and earth sciences, advection is the transport of a substance or quantity by bulk motion of a fluid. The properties of that substance are carried with it. Generally the majority of the advected substance is al ...

) 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

eigenvalue In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted b ...

s 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 Liou, M.-S., “A Sequel to AUSM: AUSM+” J. Comput. Phys., Vol. 129, 364-382, 1996. to yield a more accurate and robust version. To extend its capabilities, it has been further developed in Liou, M.-S., “A Sequel to AUSM, Part II: AUSM+-up” J. Comput. Phys., Vol. 214, 137- 170, 2006. 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 Entropy is a scientific concept, as well as a measurable physical property, that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynam ...

-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 number Mach number (M or Ma) (; ) is a dimensionless quantity in fluid dynamics representing the ratio of flow velocity past a boundary to the local speed of sound. It is named after the Moravian physicist and philosopher Ernst Mach. : \mathrm = \frac ...

s. 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 In aerodynamics, a hypersonic speed is one that exceeds 5 times the speed of sound, often stated as starting at speeds of Mach 5 and above. The precise Mach number at which a craft can be said to be flying at hypersonic speed varies, since in ...

aerodynamics Aerodynamics, from grc, ἀήρ ''aero'' (air) + grc, δυναμική (dynamics), is the study of the motion of air, particularly when affected by a solid object, such as an airplane wing. It involves topics covered in the field of fluid dyn ...

large eddy simulation Large eddy simulation (LES) is a mathematical model for turbulence used in computational fluid dynamics. It was initially proposed in 1963 by Joseph Smagorinsky to simulate atmospheric air currents, and first explored by Deardorff (1970). LES is c ...

and aero-acoustics, direct numerical simulation, multiphase flow, galactic relativistic flowWada, K. and Koda, J., “Instabilities of Spiral Shock – I. Onset of Wiggle Instability and its Mechanism,”

Monthly Notices of the Royal Astronomical Society ''Monthly Notices of the Royal Astronomical Society'' (MNRAS) is a peer-reviewed scientific journal covering research in astronomy and astrophysics. It has been in continuous existence since 1827 and publishes letters and papers reporting orig ...

, Vol. 349, 270-280 (11), 2004. etc.

References

{{DEFAULTSORT:Advection upstream splitting method Computational fluid dynamics Numerical differential equations

Features

Applications

See also

References