Conservative low-pass filter with compact stencils for hierarchical Cartesian mesh

A conservative low-pass explicit filter with compact stencils for hierarchical Cartesian mesh is proposed. The proposed filter has two key features; the primary conservation of the conservative variables (i.e., mass, momentum, and total energy) are satisfied even at non-conforming block boundaries where grid refinement level change, and the compact stencils are achieved by employing the explicit filter while the low-pass characteristic is enhanced by properly controlling the transfer function. The proposed filter is the flux-based filter and introduces the filter flux that satisfies the conservation of the conservative variables at the non-conforming block boundaries, and the appropriate control of the transfer function is achieved by controlling the filter flux. The proposed filter is coupled with the stable and non-dissipative kinetic energy and entropy preserving (KEEP) scheme for the hierarchical Cartesian mesh (Kuya and Kawai 2020) and applied to the numerical experiments of the inviscid vortex advection, Taylor–Green vortex, and turbulent wake behind a sphere. The numerical experiments demonstrate that the proposed filter conserves the conservative variables on the non-conforming mesh and successfully removes the high-wavenumber spurious oscillations while not showing any major detrimental effects on the well-resolved flows.