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：本文介绍了一种新颖的方法,用于计算以细胞为中心的保守数字方法在单元格边界上的数字通量。用于计算重建多数值法的明显梯度,由根据本文中所谓的隐含梯度,即隐含梯度,根据紧凑的有限差异计算的高阶梯度所取代。通过边界变异稀释(BVD)算法,一种问题独立的冲击捕捉法,用来抑制电流与冲击和材料界面模拟的振荡。进行了若干数字测试案例,以利用可压缩流的隐含梯度方法核实拟议方法的能力。