求解任意网格上可压缩Navier-Stokes方程的鲁棒隐式高阶间断伽辽金方法

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中文摘要：为了提高高阶方法在模拟复杂结构粘性流动时的鲁棒性和收敛性，本文提出了一种隐式高阶间断伽辽金(DG)方法。该种方法在计算稳定性和效率之间实现了良好的平衡，能够有效地处理复杂流动问题。具体地，为了求解线性系统，发展了精确雅可比矩阵求解方法，并应用于广义最小残差(GMRES)方法进行预处理和矩阵向量生成。该方法显著减少了隐式计算中雅可比矩阵的数值误差，提高了计算的准确性和稳定性。同时，通过自适应CFL数增加策略，进一步提高了隐式方法的计算效率。此外，为了提高所提出方法对复杂网格畸变的适应性，所有的模拟都在参数域中进行。这种方法显著提高了隐式计算中质量矩阵的可逆性，从而提高了计算的稳定性。本文还对影响计算稳定性和效率的各种参数进行了全面分析，包括CFL数、Krylov子空间大小和GMRES收敛标准。通过一系列测试算例，证明了将DG方法、GMRES方法、精确雅可比矩阵计算方法、自适应CFL数和参数域相结合，能够显著提高计算的鲁棒性、收敛性和计算精度。这些分析结果为高阶计算中的隐式计算提供了重要的参考价值。

外文标题：A robust implicit high-order discontinuous Galerkin method for solving compressible Navier-Stokes equations on arbitrary grids

外文摘要：The primary impediments impeding the implementation of high-order methods in simulating viscous flow over complex configurations are robustness and convergence.These challenges impose significant constraints on computational efficiency,particularly in the domain of engineering applications.To address these concems,this paper proposes a robust implicit high-order discontinuous Galerkin(DG)method for solving compressible Navier-Stokes(NS)equations on arbitrary grids.The method achieves a favorable equilibrium between computational stability and efficiency.To solve the linear system,an exact Jacobian matrix solving strategy is employed for preconditioning and matrix-vector generation in the generalized minimal residual(GMRES)method.This approach mitigates numerical errors in Jacobian solution during implicit calculations and facilitates the implementation of an adaptive Courant-Friedrichs-Lewy(CFL)number increasing strategy,with the aim of improving convergence and robustness.To further enhance the applicability of the proposed method for intricate grid distortions,all simulations are performed in the reference domain.This practice significantly improves the reversibility of the mass matrix in implicit calculations.A comprehensive analysis of various parameters influencing computational stability and efficiency is conducted,including CFL number,Krylov subspace size,and GMRES convergence criteria.The computed results from a series of numerical test cases demonstrate the promising results achieved by combining the DG method,GMRES solver,exact Jacobian matrix,adaptive CFL number,and reference domain calculations in terms of robustness,convergence,and accuracy.These analysis results can serve as a reference for implicit computation in high-order calcula-tions.

外文关键词：

Discontinuous Galerkin methodExact Jacobian matrixGMRES solverAdaptive CFL numberReference domainHigh-order

作者：

严佳、杨小权、翁培奋

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作者单位：

Shanghai Institute of Applied Mathematics and Mechanics,Shanghai Key Laboratory of Mechanics in Energy Engineering,School of Mechanics and Engineering Science,Shanghai University,Shanghai 200072,China

College of Energy and Mechanical Engineering,Shanghai University of Electric Power Shanghai 200090,China

关键词：

Discontinuous Galerkin method Exact Jacobian matrix GMRES solver Adaptive CFL number Reference domain High-order

基金：

National Natural Science Foundation of ChinaTechnology Development Program

项目编号：

12102247JCKY2022110C119

出版年：

2024

DOI：

10.1007/s10409-024-23429-x

力学学报(英文版)

CSTPCD

影响因子：0.363

ISSN：0567-7718

年,卷(期)：2024.40(8)