High Order Finite Difference Schemes on Non-uniform Meshes with Good Conservation Properties

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Symmetry-preserving discretization of turbulent flow (2003, methodology): “Depending on the choice made for the discretization of the convective term, conservation of either momentum or energy in addition to mass is achieved in [5].”
Highly energy-conservative finite difference method for the cylindrical coordinate system (2002, methodology): “This is due to an inconsistency between the differencing and interpolating operators [17].”
MicroHH 1.0: a computational fluid dynamics code for direct numerical simulation and large-eddy simulation of atmospheric boundary layer flows (2017, methodology): “The code supports second-order and fourth-order accurate discretizations following Morinishi et al. (1998) and Vasilyev (2000).”
High order conservative finite difference scheme for variable density low Mach number turbulent flows (2007, methodology): “[15] and Vasilyev [17], local kinetic energy is ambiguous to define in a staggered grid arrangement, as the velocity components are found at different locations.”
A Fully Conservative Second-Order Finite Difference Scheme for Incompressible Flow on Nonuniform Grids (2002, methodology): “In the analyses of both Morinishi et al. and Vasilyev, time advancement was accomplished by a third-order Runge–Kutta time-stepping method.”