High-order multioperators-based schemes: Developments and applications

The paper presents the developments of the schemes with multioperators-based approximations for the Euler and the Navier-Stokes equations which orders varying from 9 to 20. The claimed accuracy and resolution of the optimized schemes are illustrated using model equations. The applications to the discontinuous solutions are outlined, the solutions of the Riemann problem with the 20th-order multioperator being presented as an example. The results of high fidelity calculations of flow instabilities phenomena using optimized multioperators-based schemes are presented. They concern with hot jets instabilities manifested by forming vortex rings as well as the upstream propagation of acoustic waves in the case of slightly supersonic underexpanded jets.