CABARET SCHEMES FOR ONE-DIMENSIONAL GAS DYNAMICS EQUATIONS IN EULERIAN VARIABLES (PREPRINT IBRAE-2001-15)

Preprint IBRAE-2001-15

Goloviznin V.M., Karabasov S.A.

In the present paper we develop a few Godunov-type compact upwind difference schemes with a space split time derivative (CABARET) in application to one-dimensional compressible gas flows. As opposed to the conventional approach in improving the order of approximation by incorporating the information from adjacent space cells, we use an approach that does not lead to extending the spatial stencil. Instead the approximation accuracy is improved by using additional time layers. Adopting the first order Roe scheme as the base scheme we construct a few compact schemes which are conservative, not resulting in non-physical oscillations, and second-order accurate in the region of smooth solutions. In numerical experiment there are two shock tube problems with uniform and non-uniform space grid used. For the sake of comparison we consider several classical second-order TVD schemes. In particular, we show that the most successful of CABARETs schemes developed results in a notably better solution quality than the well-known variable extrapolation method MUSCL.   

Bibliographical reference

Goloviznin V.M., Karabasov S.A. CABARET schemes for one-dimensional gas dynamics equations in Eulerian variables (in Russian). Preprint IBRAE-2001-15. Moscow: Nuclear Safety Institute, November 2001. 20 p. — Refs.: 15 items.