Spurious numerical oscillations in simulation of supersonic flows using shock-capturing schemes

The numerical simulation of transitional and turbulent Bows in supersonic boundary layers often involves a physical process of a shock-disturbance wave interaction in complex multidimensional flowfields. For such simulations, it is required that there be a high order of accuracy in capturing the shock waves without spurious numerical disturbances. Evaluation of the numerical oscillations generated behind a stationary bow shock by using high-order shock-capturing schemes in computing multidimensional steady supersonic Bow over a circular cylinder is carried out. The numerical methods that are studied are the Total Variation Diminishing scheme and the Essentially Non-Oscillatory scheme. Although the general aerodynamic properties are appropriately captured by the shock-capturing schemes, it is shown that there are numerical oscillations in the gradients of the aerodynamic properties in the steady flowfield behind the bow shock, such as for vorticity These spurious numerical oscillations in the flowfield solution may hinder any attempt at tracking the propagation of physical disturbances behind the shock if unsteady simulations are carried out. They can be significant enough to pollute a flowfield containing small physical disturbances, It is shown that the effects of grid refinement do not reduce the oscillations but rather decrease their wavelength. it is also shown that, by roughly aligning the shock with the grid, the amplitude of these spurious oscillations can be reduced but not eliminated.