Numerical simulation of unsteady subsonic viscous gas flows based on high-order composite compact schemes

A family of high-order multioperator compact schemes for computation of viscous gas flows on curvilinear grids is considered. Depending on the number of operators used, the order of a scheme approximating the convective terms of the original equations can vary from the 6th to 22nd. The viscous terms and the metric coefficients of a generalized curvilinear coordinate system are approximated with the same order. An example of three schemes, including a five-operator one, which is the most computationally intensive in the described family, is used to examine their structure. The change in the approximation and dissipation properties of the schemes caused by an increase in their order is investigated. The schemes are used for comparative computations of subsonic gas flows based on the Euler and Navier–Stokes equations. Numerical results based on the 22nd-order scheme are presented for a viscous subsonic airfoil flow in a wide range of angles of attack and for an impermeable parachute canopy.