Flux Limited Dissipation Schemes for High Speed Unsteady Flows

Within the framework of the Local Extremum Diminishing (LED) or Essentially Local Extremum Diminishing (ELED) principle, efficient approaches to obtain a class of non-oscillatory high resolution schemes are presented. The LED principle requires that local maxima should not increase and local minima should not decrease to produce a monotonicity preserving scheme for scalar hyperbolic conservation laws. The LED constraint can be judiciously relaxed by the ELED approach to achieve high accuracy at smooth extrema. The extensions of the LED and ELED theories to systems of equations are also examined by considering several evolution processes, i.e. flux splitting methods. Higher-order dissipation schemes based on the LED or ELED principle combined with three flux splitting methods are applied to well-defined test problems that contain the essential physics of high speed unsteady flows : strong moving shocks, contact discontinuities and high expansion regions. The numerical results are carefully examined and the performance of each numerical scheme is assessed.