Numerical (error) issues on compressible multicomponent flows using a high-order differencing scheme: Weighted compact nonlinear scheme

A weighted compact nonlinear scheme (WCNS) is applied to numerical simulations of compressible multicomponent flows, and four different implementations (fully or quasi-conservative forms and conservative or primitive variables interpolations) are examined in order to investigate numerical oscillation generated in each implementation. The results show that the different types of numerical oscillation in pressure field are generated when fully conservative form or interpolation of conservative variables is selected, while quasi-conservative form generally has poor mass conservation property. The WCNS implementation with quasi-conservative form and interpolation of primitive variables can suppress these oscillations similar to previous finite volume WENO scheme, despite the present scheme is finite difference formulation and computationally cheaper for multi-dimensional problems. Series of analysis conducted in this study show that the numerical oscillation due to fully conservative form is generated only in initial flow fields, while the numerical oscillation due to interpolation of conservative variables exists during the computations, which leads to significant spurious numerical oscillations near interfaces of different component of fluids. The error due to fully conservative form can be greatly reduced by smoothing interface, while the numerical oscillation due to interpolation of conservative variables cannot be significantly reduced. The primitive variable interpolation is, therefore, considered to be better choice for compressible multicomponent flows in the framework of WCNS. Meanwhile better choice of fully or quasi-conservative form depends on a situation because the error due to fully conservative form can be suppressed by smoothed interface and because quasi-conservative form eliminates all the numerical oscillation but has poor mass conservation.