Stable and accurate schemes for the compressible Navier-Stokes equations

被引：59
|
作者：
Mattsson, K. [1 ,2 ]
Svard, M. [1 ,3 ]
Shoeybi, M. [1 ]
机构：
[1] Stanford Univ, Ctr Turbulence Res, Stanford, CA 94305 USA
[2] Uppsala Univ, Dept Informat Technol, SE-75105 Uppsala, Sweden
[3] Univ Oslo, Ctr Math Applicat, N-0316 Oslo, Norway
来源：
JOURNAL OF COMPUTATIONAL PHYSICS | 2008年 / 227卷 / 04期
关键词：
compressible; minimal stencil width schemes; Navier-Stokes equations; numerical stability; boundary conditions; second-derivatives;
D O I：
10.1016/j.jcp.2007.10.018
中图分类号：
TP39 [计算机的应用];
学科分类号：
081203 ; 0835 ;
摘要：
Minimal stencil width discretizations of combined mixed and non-mixed second-order derivatives are analyzed with respect to accuracy and stability. We show that these discretizations lead to stability for Cauchy problems. With a careful boundary treatment, we also show that the stability holds for initial-boundary value problems. The analysis is verified by numerical simulations of Burgers' and Navier-Stokes equations in two and three space dimensions. (c) 2007 Elsevier Inc. All rights reserved.
引用
收藏
页码：2293 / 2316
页数：24
相关论文
共 50 条
  • [1] STABLE AND SPECTRALLY ACCURATE SCHEMES FOR THE NAVIER-STOKES EQUATIONS
    Jia, Jun
    Liu, Jie
    [J]. SIAM JOURNAL ON SCIENTIFIC COMPUTING, 2011, 33 (05): : 2421 - 2439
  • [2] Boltzmann schemes for the compressible Navier-Stokes equations
    Ohwada, T
    [J]. RAREFIED GAS DYNAMICS, 2001, 585 : 321 - 328
  • [3] Bicompact Schemes for Compressible Navier-Stokes Equations
    Bragin, M. D.
    [J]. DOKLADY MATHEMATICS, 2023, 107 (01) : 12 - 16
  • [4] Discontinuous Galerkin schemes for the compressible Navier-Stokes equations
    Drozo, C
    Borrel, M
    Lerat, A
    [J]. SIXTEENTH INTERNATIONAL CONFERENCE ON NUMERICAL METHODS IN FLUID DYNAMICS, 1998, 515 : 266 - 271
  • [5] FLUX-LIMITED SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS
    TATSUMI, S
    MARTINELLI, L
    JAMESON, A
    [J]. AIAA JOURNAL, 1995, 33 (02) : 252 - 261
  • [6] New Unconditionally Stable Schemes for the Navier-Stokes Equations
    Yao, Hui
    Azaiez, Mejdi
    Xu, Chuanju
    [J]. COMMUNICATIONS IN COMPUTATIONAL PHYSICS, 2021, 30 (04) : 1083 - 1117
  • [7] HIGHER-ORDER-ACCURATE UPWIND SCHEMES FOR SOLVING THE COMPRESSIBLE EULER AND NAVIER-STOKES EQUATIONS
    YAMAMOTO, S
    DAIGUJI, H
    [J]. COMPUTERS & FLUIDS, 1993, 22 (2-3) : 259 - 270
  • [8] Higher-order-accurate upwind schemes for solving the compressible Euler and Navier-Stokes equations
    Yamamoto, S.
    Daiguji, H.
    [J]. Computers and Fluids, 1993, 22 (2-3): : 259 - 270
  • [9] Convergence of the relaxed compressible Navier-Stokes equations to the incompressible Navier-Stokes equations
    Ju, Qiangchang
    Wang, Zhao
    [J]. APPLIED MATHEMATICS LETTERS, 2023, 141
  • [10] SHOCK-WAVES FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS ARE STABLE
    LIU, TP
    [J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1986, 39 (05) : 565 - 594
12345