Resolving Confusions over Third-Order Accuracy of Unstructured MUSCL

In this paper, we discuss the U-MUSCL reconstruction scheme -- an unstructured-grid extension of Van Leer's kappa-scheme proposed by Burg for edge-based discretization [AIAA Paper 2005-4999]. This technique has been widely used in practical fluid-dynamics solvers but with confusions: e.g., third-order accuracy kappa=1/2 or kappa=1/3. paper clarifies some these can be accurate point-valued solution kappa=1/3 on regular grids linear equations all dimensions, it as QUICK one dimension. It is shown that cannot nonlinear equations, except a very special case simplex-element grids, low-dissipation second-order scheme. also extrapolates quadratic function exactly arbitrary provided gradient computed least-squares method. Two techniques are discussed, which transform into being genuinely grid: efficient flux-reconstruction method and source term quadrature formula kappa=1/2.