Spurious Mass Flux at Solid Wall in Euler and Navier–Stokes Computations

The reasons for a spurious mass flux through a solid wall in the Navier–Stokes computations caused by the velocity reconstruction and isothermal wall implementation are discussed. Reconstruction of Cartesian velocity components are found to cause a spurious mass flux through the wall. Based on analysis of the analytic equations, interpolation of the normal and tangent velocities is shown to fix this problem. Additionally, reconstruction of Cartesian velocity components is shown to cause numerical solution to be dependent of the reference frame while using of the normal and tangent velocities corrects this behavior. Two types of the isothermal wall implementation are considered. The first type uses the equation of state to calculate the density in ghost cells for computing both the inviscid and viscous fluxes. The second implementation uses two different sets of values in ghost cells for computing the inviscid and viscous fluxes without employing the equation of state. The first implementation is explained to create spurious mass flux through the wall while the second one ensures solid wall non-permeability. Test computations of a flow around a cylinder demonstrated that the first type does not allow predicting the shock stand-off distance with an acceptable accuracy when using the Harten–Lax–van Leer solver. The second implementation yields the stand-off distance with an acceptable accuracy of regardless of the Riemann solver used.