论文标题
基于梯度的重建：无粘性和粘性通量离散，冲击捕获及其应用于单个和多组分流
Gradient Based Reconstruction: Inviscid and viscous flux discretizations, shock capturing, and its application to single and multicomponent flows
论文作者
论文摘要
本文介绍了一种基于梯度的重建方法，用于模拟可压缩单物种和多物种Navier-Stokes方程。所提出的算法的新特征是通过无粘性和粘性方案之间的衍生物共享的有效重建：高度准确的显式和隐式梯度用于以导数表示的溶液重建。正如几个粘性流验证案例所证明的那样，将速度成分的较高级准确梯度重新计算粘性通量，并显着提高溶液和梯度质量。粘性方案是四阶精确且具有高频阻尼特性的精确设计，该特性已被确定为具有冲击波稳定的可压流模拟的至关重要的特性[Chararthi等，JCP，2022年]。使用单调性（MP）方案捕获冲击和物质不连续性，这也可以通过重复使用梯度来改善。对于Inviscid测试用例，对于非线性问题，提出的方案是线性和二阶精确度的四阶。为了证明所提出的方法的精确性和鲁棒性，提供了用于复杂粘性流的模拟的几个数值结果。
This paper presents a gradient-based reconstruction approach for simulations of compressible single and multi-species Navier-Stokes equations. The novel feature of the proposed algorithm is the efficient reconstruction via derivative sharing between the inviscid and viscous schemes: highly accurate explicit and implicit gradients are used for the solution reconstruction expressed in terms of derivatives. The higher-order accurate gradients of the velocity components are reused to compute the viscous fluxes for efficiency and significantly improve the solution and gradient quality, as demonstrated by several viscous-flow test cases. The viscous schemes are fourth-order accurate and carefully designed with a high-frequency damping property, which has been identified as a critically important property for stable compressible-flow simulations with shock waves [Chamarthi et al., JCP, 2022]. Shocks and material discontinuities are captured using a monotonicity-preserving (MP) scheme, which is also improved by reusing the gradients. For inviscid test cases, The proposed scheme is fourth-order for linear and second-order accurate for non-linear problems. Several numerical results obtained for simulations of complex viscous flows are presented to demonstrate the accuracy and robustness of the proposed methodology.
