Non-conservative and conservative formulations of characteristics-based numerical reconstructions for incompressible flows

An investigation of characteristics-based (CB) schemes for solving the incompressible Navier–Stokes equations in conjunction with the artificial-compressibility approach, is presented. Both non-conservative and conservative CB numerical reconstructions are derived and their accuracy and convergence properties are assessed analytically and numerically. We demonstrate by means of eigenvalue analysis that there are differences in the spectral characteristics of these formulations that result in different convergence properties. Numerical tests for two- and three-dimensional flows reveal that the two formulations provide similar accuracy but the non-conservative formulation converges faster