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首页> 外文期刊>Journal of Computational Physics >Reconstructed discontinuous Galerkin methods for compressible flows based on a new hyperbolic Navier-Stokes system
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Reconstructed discontinuous Galerkin methods for compressible flows based on a new hyperbolic Navier-Stokes system

机译：基于新的双曲线Navier-Stokes系统，重建了不连续的Galerkin方法，用于压缩流动

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A new first-order hyperbolic system (FOHS) is formulated for the compressible NavierStokes equations. The resulting hyperbolic Navier-Stokes system (HNS), termed HNS20G in this paper, introduces the gradients of density, velocity, and temperature as auxiliary variables. Efficient, accurate, compact and robust reconstructed discontinuous Galerkin (rDG) methods are developed for solving this new HNS system. The newly introduced variables are recycled to obtain the gradients of the primary variables. The gradients of these gradient variables are reconstructed based on a newly developed variational formulation in order to obtain a higher order polynomial solution for these primary variables without increasing the number of degrees of freedom. The implicit backward Euler method is used to integrate solution in time for steady flow problems, while the third-order explicit first stage singly diagonally Runge-Kutta (ESDIRK) time marching method is implemented for advancing solutions in time for unsteady flows. The flux Jacobian matrices are obtained with an automatic differentiation toolkit TAPENADE. The approximate system of linear equations is solved with either symmetric Gauss-Seidel (SGS) method or general minimum residual (GMRES) algorithm with a lower-upper symmetric Gauss-Seidel (LU-SGS) preconditioner. A number of test cases are presented to assess accuracy and performance of the newly developed HNS+rDG methods for both steady and unsteady compressible viscous flows. Numerical experiments demonstrate that the developed HNS+rDG methods are able to achieve the designed order of accuracy for both primary variables and the their gradients, and provide an attractive and viable alternative for solving the compressible Navier-Stokes equations. (C) 2020 Elsevier Inc. All rights reserved.
机译：对于可压缩的NavierStokes方程，建立了一个新的一阶双曲型方程组（FOHS）。由此产生的双曲线Navier-Stokes系统（HNS）在本文中称为HNS20G，它引入了密度、速度和温度梯度作为辅助变量。为了求解这种新的HNS系统，提出了高效、精确、紧凑和鲁棒的重构间断伽辽金（rDG）方法。新引入的变量被循环使用，以获得主变量的梯度。为了在不增加自由度的情况下获得这些主要变量的高阶多项式解，基于新发展的变分公式重构这些梯度变量的梯度。对于定常流动问题，采用隐式后向欧拉法进行时间积分，而对于非定常流动问题，采用三阶显式第一阶段单对角龙格-库塔（ESDIRK）时间推进法进行时间推进。通量雅可比矩阵由自动微分工具TAPENADE获得。线性方程组的近似解可采用对称高斯-赛德尔（SGS）方法或带有上下对称高斯-赛德尔（LU-SGS）预处理器的广义最小残差（GMRES）算法。本文给出了一些测试实例，以评估新开发的HNS+rDG方法在稳态和非稳态可压缩粘性流中的精度和性能。数值实验表明，所发展的HNS+rDG方法能够实现主变量及其梯度的设计精度，为求解可压缩Navier-Stokes方程提供了一种有吸引力的可行方法。（C） 2020爱思唯尔公司版权所有。

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