Remote Access Mathematics of Computation
Green Open Access

Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)

 

 

On some numerical schemes for transonic flow problems


Author: Marco Mosché Mostrel
Journal: Math. Comp. 52 (1989), 587-613
MSC: Primary 65M05; Secondary 76H05
DOI: https://doi.org/10.1090/S0025-5718-1989-0955752-2
MathSciNet review: 955752
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: New second-order accurate finite difference approximations for a class of nonlinear PDE's of mixed type, which includes the 2D Low Frequency Transonic Small Disturbance equation (TSD) and the 2D Full Potential equation (FP), are presented.

For the TSD equation, the scheme is implemented via a time splitting algorithm; the inclusion of flux limiters keeps the total variation nonincreasing and eliminates spurious oscillations near shocks. Global Linear Stability, Total Variation Diminishing and Entropy Stability results are proven. Numerical results for the flow over a thin airfoil are presented. Current techniques used to solve the TSD equation may easily be extended to second-order accuracy by this method.

For the FP equation, the new scheme requires no subsonic/supersonic switching and no numerical flux biasing. Global Linear Stability for all values of the Mach number is proven.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Mathematics of Computation with MSC: 65M05, 76H05

Retrieve articles in all journals with MSC: 65M05, 76H05


Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1989-0955752-2
Keywords: Full potential equation, transonic small disturbance equation, transonic flow, entropy condition, difference approximations
Article copyright: © Copyright 1989 American Mathematical Society