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

翻译：在本文中,我们讨论U-MUSSCL重建计划 -- -- Van Leer的 kappa- scheme 的无结构的网格延伸 -- -- Burg 提议的Van Leer的 kappa- scheme -- -- 由Burg提出,用于基于边缘的离异化[AIAAA Paper 2005-4999]。这一技术被广泛用于实用的不结构的电网流流动力学解答器中,但有混淆:例如,使用 kappa=1/2 或 kappa=1/3 的三阶梯子对非线式方程式不能准确达到三阶梯子。本文澄清了其中的一些混淆:例如,U-MUSL 计划在点值解决方案中可能是三阶梯度准确的三阶梯度,而 kappa=1 的二次电路流法则是一个任意的平流法函数。