A total variation minimizing numerical method for predicting oscillation free solutions to flows with shocks
Abstract
A novel approach has been developed for the solution of the nonlinear equations of gas dynamics that incorporates a minimization procedure to provide a near oscillation free solution. The single alpha per face formulation of this total variation minimizing numerical method uses a parameter at each cell face to linearly combine two second-order accurate schemes with opposite phase error characteristics to produce a hybrid scheme that exhibits minimum dispersion. For the one-dimensional problems studied, the scheme produced smooth, nearly monotone solutions with almost no additional computer time than existing schemes. Results have been presented for the one-dimensional wave equation, Burgers' equation and Euler equations.
- Publication:
-
AIAA, Aerospace Sciences Meeting
- Pub Date:
- January 1990
- Bibcode:
- 1990aiaa.meetQ....I
- Keywords:
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- Burger Equation;
- Computational Fluid Dynamics;
- Gas Dynamics;
- Oscillating Flow;
- Shock Waves;
- Euler Equations Of Motion;
- Wave Equations;
- Fluid Mechanics and Heat Transfer