Adaptive-quadrature fluctuation-splitting schemes for the Euler equations

Abstract

In this paper, we present fluctuation-splitting schemes that can capture an isolated shock over a suitably oriented single triangular element and also recognize a rarefaction. A particular focus is on the evaluation of the fluctuation (or the cell residual): a one-parameter-family quadrature rule is employed to evaluate the fluctuation, which endows the fluctuation with a wave recognition capability. The parameter value is chosen based on the nature of the nonlinear wave passing through the element, and then the resulting fluctuation is distributed to the nodes. This strategy, combined with various distribution schemes, defines a family of adaptive-quadrature fluctuation-splitting schemes. The results demonstrate the superior ability of the new schemes in handling nonlinear waves compared with standard fluctuation-splitting schemes that cannot capture shocks over a single element and also admits nonphysical shocks unless some kind of entropy fix is incorporated. Copyright © 2007 John Wiley & Sons, Ltd.