A stable and non-dissipative numerical scheme for Cartesian methods is proposed. The proposed scheme is based on the second-order kinetic energy and entropy preserving scheme, which the authors proposed recently, and conservation is satisfied at non-conforming boundaries where the grid refinement level is different across the computational block boundaries. In the proposed scheme, ghost cells are used at computational block boundaries for efficient parallel computation, and conservation is satisfied by assigning appropriate values to the ghost cells. Also, although the five conservative variables (i.e., mass, momentum, and total energy) are typically transferred from computational cells to corresponding ghost cells at computational block boundaries, the proposed scheme transfers two more conservative variables to satisfy conservation at non-conforming block boundaries. In a vortex convection test, the convergence rates of the L2- and L∞-error norms are examined, and the proposed scheme preserves the second-order of accuracy without inducing destructive errors at non-conforming boundaries. In an inviscid Taylor-Green vortex simulation, the proposed scheme demonstrates superior numerical stability by preserving kinetic energy and entropy. Also, the proposed scheme performs more stable computations on a non-conforming computational grid than a typical kinetic energy preserving scheme calculated on a uniform computational grid.
- Cartesian grid method
- Compressible flows
- Kinetic energy and entropy preservation
- Non-conforming block boundary
- Split convective forms