This paper introduces a novel approach to compute the numerical fluxes at the cell boundaries for a cell-centered conservative numerical scheme. Explicit gradients used in deriving the reconstruction polynomials are replaced by high-order gradients computed by compact finite differences, referred to as implicit gradients in this paper. A problem-independent shock capturing approach via Boundary Variation Diminishing (BVD) algorithm is used to suppress oscillations for the simulation of flows with shocks and material interfaces. Several numerical test cases are carried out to verify the proposed method's capability using the implicit gradient method for compressible flows.

翻译：本文提出了一种新颖的方法，用于计算单元中心守恒数值格式中单元边界处的数值通量。推导重构多项式时所用的显式梯度被由紧致有限差分计算的高阶梯度所替代，在本文中称为隐式梯度。采用基于边界变差减小（BVD）算法的与问题无关的激波捕捉方法，以抑制含激波与物质界面流动模拟中的振荡。通过若干数值算例，验证了所提出的基于隐式梯度方法在可压缩流动中的能力。