High-order accurate kinetic-energy and entropy preserving (KEEP) schemes on curvilinear grids

被引:20
作者
Kuya, Yuichi [1 ]
Kawai, Soshi [1 ]
机构
[1] Tohoku Univ, Dept Aerosp Engn, Aoba Ku, 6-6-01 Aramaki Aza Aoba, Sendai, Miyagi 9808579, Japan
基金
日本学术振兴会;
关键词
Finite difference schemes; Kinetic energy and entropy preservation; Split convective forms; High-order accurate schemes; Generalized curvilinear coordinates; Shock-free compressible flows; LARGE-EDDY SIMULATION; DIRECT NUMERICAL-SIMULATION; FINITE-DIFFERENCE SCHEMES; CONVECTIVE TERMS; TURBULENCE; FLOW; CONSERVATION; FORMULATIONS; PROPERTY; FORM;
D O I
10.1016/j.jcp.2021.110482
中图分类号
TP39 [计算机的应用];
学科分类号
081203 ; 0835 ;
摘要
High-order accurate kinetic energy and entropy preserving (KEEP) schemes in generalized curvilinear coordinates are proposed for stable and non-dissipative numerical simulations. The proposed schemes are developed on the basis of the physical relation that the fluxes in the Euler equations in generalized curvilinear coordinates can be derived by taking the inner product between the inviscid fluxes and the area vectors used for the coordinate transformation. To satisfy this physical relation discretely, this study proposes to interpret the area vector components as another individual variable and discretize the area vectors in the same way as other physical variables, such as the density and velocity. Consequently, the convective and pressure-related terms are discretized in a new split convective form, "quartic split form", and quadratic split form, respectively. The high-order extension is straightforward, referring to the high-order formulations proposed for kinetic energy preserving schemes in a previous study. Numerical tests of vortex convection, inviscid Taylor-Green vortex, and turbulent boundary layer flow are conducted to assess the order of accuracy, the kinetic energy and entropy preservation property, and numerical robustness of the proposed KEEP schemes. The proposed high-order accurate KEEP schemes successfully perform long-time stable computations without numerical dissipation by preserving the total kinetic energy and total entropy well, even on a largely-distorted computational grid. (C) 2021 Elsevier Inc. All rights reserved.
引用
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页数:35
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共 45 条
[31]  
Obayashi S., 1988, Tech. Rep. NASA-TM-100042, A-88027
[32]   A low numerical dissipation patch-based adaptive mesh refinement method for large-eddy simulation of compressible flows [J].
Pantano, C. ;
Deiterding, R. ;
Hill, D. J. ;
Pullin, D. I. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2007, 221 (01) :63-87
[33]   Semi-local scaling and turbulence modulation in variable property turbulent channel flows [J].
Patel, Ashish ;
Peeters, Jurriaan W. R. ;
Boersma, Bendiks J. ;
Pecnik, Rene .
PHYSICS OF FLUIDS, 2015, 27 (09)
[34]   Turbulence in supersonic boundary layers at moderate Reynolds number [J].
Pirozzoli, Sergio ;
Bernardini, Matteo .
JOURNAL OF FLUID MECHANICS, 2011, 688 :120-168
[35]   Stabilized non-dissipative approximations of Euler equations in generalized curvilinear coordinates [J].
Pirozzoli, Sergio .
JOURNAL OF COMPUTATIONAL PHYSICS, 2011, 230 (08) :2997-3014
[36]   Generalized conservative approximations of split convective derivative operators [J].
Pirozzoli, Sergio .
JOURNAL OF COMPUTATIONAL PHYSICS, 2010, 229 (19) :7180-7190
[37]   GPU accelerated flow solver for direct numerical simulation of turbulent flows [J].
Salvadore, Francesco ;
Bernardini, Matteo ;
Botti, Michela .
JOURNAL OF COMPUTATIONAL PHYSICS, 2013, 235 :129-142
[38]   Preventing spurious pressure oscillations in split convective form discretization for compressible flows [J].
Shima, Nao ;
Kuya, Yuichi ;
Tamaki, Yoshiharu ;
Kawai, Soshi .
JOURNAL OF COMPUTATIONAL PHYSICS, 2021, 427
[39]   Direct numerical simulation of high-speed transition due to an isolated roughness element [J].
Subbareddy, Pramod K. ;
Bartkowicz, Matthew D. ;
Candler, Graham V. .
JOURNAL OF FLUID MECHANICS, 2014, 748 :848-878
[40]   A fully discrete, kinetic energy consistent finite-volume scheme for compressible flows [J].
Subbareddy, Pramod K. ;
Candler, Graham V. .
JOURNAL OF COMPUTATIONAL PHYSICS, 2009, 228 (05) :1347-1364