Convergence issues in using high‐resolution schemes and lower–upper symmetric Gauss–Seidel method for steady shock‐induced combustion problems
Convergence issues in using high‐resolution schemes and lower–upper symmetric Gauss–Seidel method for steady shock‐induced combustion problems
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DOI：
10.1002/fld.3718
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发表时间：
2013-04
影响因子：
1.8
通讯作者：
Bin Li;Li Yuan
中科院分区：
文献类型：
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作者：
Bin Li;Li Yuan
本文报道了用高分辨率激波捕捉格式模拟稳态激波诱导燃烧问题的数值收敛研究。采用了五种典型格式：基于Roe通量的单调上游中心守恒律格式(MUSCL)和加权基本无振荡格式(WENO)，基于Lax-Friedrichs分裂的无振荡无自由参数耗散(NND)和WENO格式，以及Harten-Yee迎风总变分减小(TVD)格式。格式采用结构四边形网格的有限体积逐维离散和解轴对称多组分反应N-S方程的上-下对称Gauss-Seidel(LU-SGS)松弛方法。以马赫数M=3.55和6.46的球形弹丸和M=6.7的冲压加速器为例，对不同格式的迭代收敛进行了比较。这些试验案例在文献中被认为是稳态燃烧问题。对逐步细化网格的计算表明，对于M=3.55的激波和燃烧锋面分离的情况，二阶NND、MUSCL和TVD格式可以很好地从粗到细收敛到稳态，而(名义上)五阶WENO格式只能收敛到一定的残差水平。更有趣的是，数值结果表明，对于球面弹丸中的M=6.46和在冲压加速器情况下的细网格上的M=6.7，所有格式都不收敛到稳态解，尽管它们都收敛到较粗的网格或没有化学反应的细网格上。这一结果是基于LU-SGS方案的特定预条件的。讨论了反应流模拟不收敛的可能原因。版权所有-2012 John Wiley&Sons，Ltd.
This paper reports numerical convergence study for simulations of steady shock‐induced combustion problems with high‐resolution shock‐capturing schemes. Five typical schemes are used: the Roe flux‐based monotone upstream‐centered scheme for conservation laws (MUSCL) and weighted essentially non‐oscillatory (WENO) schemes, the Lax–Friedrichs splitting‐based non‐oscillatory no‐free parameter dissipative (NND) and WENO schemes, and the Harten–Yee upwind total variation diminishing (TVD) scheme. These schemes are implemented with the finite volume discretization on structured quadrilateral meshes in dimension‐by‐dimension way and the lower–upper symmetric Gauss–Seidel (LU–SGS) relaxation method for solving the axisymmetric multispecies reactive Navier–Stokes equations. Comparison of iterative convergence between different schemes has been made using supersonic combustion flows around a spherical projectile with Mach numbers M = 3.55 and 6.46 and a ram accelerator with M = 6.7. These test cases were regarded as steady combustion problems in literature. Calculations on gradually refined meshes show that the second‐order NND, MUSCL, and TVD schemes can converge well to steady states from coarse through fine meshes for M = 3.55 case in which shock and combustion fronts are separate, whereas the (nominally) fifth‐order WENO schemes can only converge to some residual level. More interestingly, the numerical results show that all the schemes do not converge to steady‐state solutions for M = 6.46 in the spherical projectile and M = 6.7 in the ram accelerator cases on fine meshes although they all converge on coarser meshes or on fine meshes without chemical reactions. The result is based on the particular preconditioner of LU–SGS scheme. Possible reasons for the nonconvergence in reactive flow simulation are discussed.Copyright © 2012 John Wiley & Sons, Ltd.