Third-order less oscillatory and less diffusive compact stencil-based upwind schemes, and their applications to incompressible flows and free surface flows

We propose novel third-order less oscillatory and diffusive compact stencil-based upwind schemes for the approximation of continuity equation. The proposed are based on constrained interpolation profile-conservative semi-Lagrangian schemes. An important feature is that functions constructed using only variables within one cell (a average two boundary values). Furthermore, have accuracy also oscillatory, diffusive, fully conservative. validated through various benchmark problems comparisons with experiments droplets collision/separation droplet splashing. numerical results shown smooth solution, capture discontinuities solutions simultaneously without oscillations. can secondary vorticity lid-driven cavity flow Re = 7500 a Cartesian grid 64 × 64. 40 show reproduce quite coarse grids. These splashing demonstrated reduce diffusions well against existing robust.