A natural conservative flux difference splitting for the hyperbolic systems of gasdynamics
Abstract
Gasdynamic hyperbolic systems are treated by a novel conservative flux difference splitting upwind method which is applicable to explicit or implicit and iterative or direct schemes, for marching in time or space with the Euler or compressible NavierStokes equations. The method is able to capture sharp shocks correctly by maintaining global conservation. The embedded characteristics formulation is cast in the volumetric internal energy primitive variable, which is effective for real as well as perfect gases. Higher order upwind formulae are constructed from the distribution of pieces of the simple internal flux difference splitting, and the method reverts to first order at the appropriate points in order not to violate the domain of dependence by differencing across discontinuities. At insignificant computational overhead, switching is done by simple algebraic extensions of the truth functions that determine upwind direction for the first order scheme.
 Publication:

American Institute of Aeronautics and Astronautics Conference
 Pub Date:
 June 1982
 Bibcode:
 1982aiaa.confV....L
 Keywords:

 Computational Fluid Dynamics;
 Finite Difference Theory;
 Flux Quantization;
 Gas Dynamics;
 Hyperbolic Systems;
 Splitting;
 Conservation Equations;
 Eigenvalues;
 Eigenvectors;
 NavierStokes Equation;
 Nonconservative Forces;
 Fluid Mechanics and Heat Transfer