Criteria for the design of limiters yielding efficient high resolution TVD schemes

Abstract—High resolution, finite-volume, conservative schemes, based on the classical MUSCL (Mono-tonic Upwind Schemes for Conservation Laws) construction and non-linear interpolation limiters are considered. Possible criteria are established for the construction of the limiters, yielding monotonic and ecient schemes. For scalar hyperbolic conservation laws, new limiters for both upwind and centred numerical flux functions are proposed and compared with existing limiters. These limiters are also com-pared in the case of the computation of the two-dimensional inviscid flow around a NACA0012 airfoil with particular attention to the issues of iterative convergence to steady state and monotonicity preser-vation of the computed solution. We actually show that the proposed criteria do control these issues