Characteristic-based flux limiters of an essentially third-order flux-splitting method for hyperbolic conservation laws

✍ Scribed by Herng Lin; Ching-Chang Chieng

• Publisher: John Wiley and Sons
• Year: 1991
• Tongue: English
• Weight: 974 KB
• Volume: 13
• Category: Article
• ISSN: 0271-2091
• DOI: 10.1002/fld.1650130303

✦ Synopsis

A flux limiter based on characteristic variables is extended by a control volume flux formulation to approximate the convection term at the cell interface for an essentially third-order-accurate scheme. The basic algorithm uses implicit MUSCL-type flux splitting and the approximate factorization method. It is applied to three test problems: (i) a one-dimensional shock tube problem; (ii) a two-dimensional problem of an oblique shock step with Mach numbers 3 and 10 and a shock angle of 59"; (iii) a two-dimensional problem of transonic inviscid flow past an NACA0012 aerofoil with Mach number D8 at zero angle of attack. The computational results by the new flux limiter function are compared with the results of direct applications of the SMART algorithm, Leonard's SHARP algorithm, the third-order Van Leer flux-splitting method with a smooth limiter, Harten's second-order unwind-biased TVD scheme, Chakravarthy's third-order MUSCLtype TVD scheme and the exact solution. The comparison shows that the present method gives the most accurate and least oscillatory results with a rapid rate of convergence.