Grid Convergence Analysis for MUSCL-based Numerical Scheme in Shockwave-containing Flows

Abstract

This paper investigated the influence of limiter functions widely utilized in MUSCL-type (Monotone Upstream-centred Schemes for Conservation Laws) upwind numerical schemes on the solution accuracy of shockwave-containing flows. An incident shock interacting with laminar boundary layer developed on a flat plate was numerically simulated with the in-house developed code. A mixed-order grid convergence study was performed to assess the spatial errors of different limiters in simulating the selected shockwave-containing flow on flat plate. The conclusions are that, limiter functions implemented in the current in-house code play the critical roles in accurately predicting shockwave-containing flows. The mixed-order error estimator based on grid convergence study was proved to be applicable to evaluate the spatial errors of shockwave-containing flows, where the shock could reduce the nominal second- or third-order accuracy to first-order. The mixed-order estimator is conservative in the sense that the actual error is less than the error estimated, in the examined case.