# Mach-uniform algorithm with coupled pressure and temperature corrections

## Description

A low Mach number formulation of AUSM+ is obtained by adding a pressure difference stabilisation term to the expression of the face velocity. This properly scaled term allows the accurate solution of steady low Mach number flows of a compressible fluid. It is switched off for large Mach numbers. A coupled pressure and temperature correction algorithm is proposed with corrections derived from the continuity equation and the energy equation. This algorithm allows the solution of steady temperature difference driven flow of a compressible fluid at a very low Mach number. For adiabatic flow, the temperature correction may be switched off. The algorithm reduces then to a pressure correction algorithm with corrections derived from the energy equation.

## Publications

NERINCKX K., VIERENDEELS J., DICK E.: Mach-uniformity through the coupled pressure and temperature correction algorithm. J. of Computational Physics, 206 (2005), 597-623.

NERINCKX K., VIERENDEELS J., DICK E.: A pressure-correction algorithm with Mach-uniform efficiency and accuracy. Int. J. for Numerical Methods in Fluids, 47 (2005), 1205-1211.

NERINCKX K., VIERENDEELS J., DICK E.: A Mach-uniform algorithm pressure correction algorithm with AUSM+ flux definitions. Int. J. of Numerical Methods for Heat and Fluid Flow, 16 (2006), 718-739.

NERINCKX K., VIERENDEELS J., DICK E.: A Mach-uniform algorithm: Coupled versus segregated approach. J. of Computational Physics, 224 (2007), 314-331.

NERINCKX K., VIERENDEELS J., DICK E.: Three Mach-uniform algorithms.

J. of Computational and Applied Mathematics, 215 (2008), 521-527.