Flux-limited schemes for the compressible Navier-Stokes equations
Flux-limited schemes for the compressible Navier-Stokes equations
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DOI：
10.2514/3.12422
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发表时间：
1995-02
期刊：
影响因子：
2.5
通讯作者：
S. Tatsumi;L. Martinelli;A. Jameson
中科院分区：
文献类型：
--
作者：
S. Tatsumi;L. Martinelli;A. Jameson
为了提高完全可压缩Navier-Stokes方程解的精度，本文提出了几种高分辨率格式。在亚音速，跨音速和超音速的层流边界层的计算进行了验证所提出的计划。它的结论是，这些计划，这是原来量身定制的非振荡激波捕捉，粘性流产生精确的解决方案。本研究的结果表明，制定的限制过程是更重要的比选择一个特定的通量分裂技术，在确定计算的粘性流的准确性。对称有限正格式和上游有限正格式有望提高结果的精度，特别是在粗网格上。在跨音速、超音速和高超音速马赫数下可压缩流的HE计算要求采用无振荡离散格式，这种格式将高精度与激波和接触间断的高分辨率结合起来。这些计划还必须制定在这样一种方式，他们方便处理复杂的几何形状。在过去的十年中，许多计划已经开发，以满足这些要求，结合欧拉方程的解决方案。l最近，应用这些计划的Navier-Stokes方程已经产生的算法，已逐步获得认可的分析工具，在航空航天工业。然而，仍然需要理解和改进Navier-Stokes格式，使其超越现有技术水平。最令人信服的原因在于，激波捕获需要构造数值耗散的格式，这一要求可能影响物理粘性问题解的全局精度。Jameson在最近的一篇论文[2]中指出，基于局部极值递减（LED）原理，即最大值不应增加，最小值不应减少，可以为标量守恒律发展一种非振荡格式理论。此外，虽然它是等效的总变差递减原理（TVD）的一维问题，LED原则可以自然地应用到多维问题的结构化和非结构化网格。这一最新进展揭示了高分辨率开关和通量限制耗散方案的基本原理。特别是，它允许新制定的两个家庭的通量限制计划命名，对称有限的积极（SLIP）和上游有限的积极（USLIP），分别。目前的工作合并了几个耗散计划的基础上的SLIP和USLIP建设与一个发达的细胞为中心，有限体积制定解决二维Navier-Stokes方程。3的目的是分析和验证这些新的离散粘性流问题的解决方案。节中综述了标量对流方程的非振子y离散近似的设计原理
Several high-resolution schemes are formulated with the goal of improving the accuracy of solutions to the full compressible Navier-Stokes equations. Calculations of laminar boundary layers at subsonic, transonic, and supersonic speeds are carried out to validate the proposed schemes. It is concluded that these schemes, which were originally tailored for nonoscillatory shock capturing, yield accurate solutions for viscous flows. The results of this study suggest that the formulation of the limiting process is more important than the choice of a particular flux splitting technique in determining the accuracy of computed viscous flows. Symmetric limited positive and upstream limited positive schemes hold the promise of improving the accuracy of the results, especially on coarser grids. HE calculation of compressible flows at transonic, supersonic, and hypersonic Mach numbers requires the implementation of nonoscillatory discrete schemes which combine high accuracy with high resolution of shock waves and contact discontinuities. These schemes must also be formulated in such a way that they facilitate the treatment of complex geometric shapes. In the past decade numerous schemes have been developed to meet these requirements in conjunction with the solution of the Euler equations.l More recently, the application of such schemes to the Navier-Stokes equations has produced algorithms which have progressively gained acceptance as analysis tools in the aerospace industry. There remains, however, a need to understand and improve Navier-Stokes schemes beyond the current state of the art. The most compelling reason for this rests on the fact that shock capturing requires the construction of schemes which are numerically dissipative, a requirement which could affect the global accuracy of the solution of the physical viscous problem. In a recent paper2 Jameson has shown that a theory of nonoscillatory schemes can be developed for scalar conservation laws based upon the local extremum diminishing (LED) principle that maxima should not increase and minima should not decrease. Moreover, although it is equivalent to the total variation diminishing principle (TVD) for one-dimensional problems, the LED principle can be applied naturally to multidimensional problems on both structured and unstructured meshes. This recent development has shed new light on the principles underlying the construction of both high-resolution switched and flux-limited dissipation schemes. In particular, it allowed the new formulation of two families of flux-limited schemes denominated, symmetric limited positive (SLIP) and upstream limited positive (USLIP), respectively. The present work merges several dissipation schemes based on both the SLIP and USLIP construction with a well-developed cell-centered, finite-volume formulation for solving the two-dimensional Navier-Stokes equations.3 The aim is to analyze and validate these new discretizations for the solution of viscous flow problems. In Sec. II the design principles of nonoscillator y discrete approximations to a scalar convection equation are reviewed together