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首页> 外文学位 >Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow.
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Multi-dimensional upwind fluctuation splitting scheme with mesh adaption for hypersonic viscous flow.

机译：基于网格的多维迎风涨落分裂方案，适用于高超声速粘性流。

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摘要

A multi-dimensional upwind fluctuation splitting scheme is developed and implemented for two dimensional and axisymmetric formulations of the Navier-Stokes equations on unstructured meshes. Key features of the scheme are the compact stencil, full upwinding, and non-linear discretization which allow for second-order accuracy with enforced positivity. Throughout, the fluctuation splitting scheme is compared to a current state-of-the-art finite volume approach, a second-order, dual mesh upwind flux difference splitting scheme (DMFDSFV), and is shown to produce more accurate results using fewer computer resources for a wide range of test cases. The scalar test cases include advected shear, circular advection, non-linear advection with coalescing shock and expansion fans, and advection-diffusion. For all scalar cases the fluctuation splitting scheme is more accurate, and the primary mechanism for the improved fluctuation splitting performance is shown to be the reduced production of artificial dissipation relative to DMFDSFV. The most significant scalar result is for combined advection-diffusion, where the present fluctuation splitting scheme is able to resolve the physical dissipation from the artificial dissipation on a much coarser mesh than DMFDSFV is able to, allowing order-of-magnitude reductions in solution time. Among the inviscid test cases the converging supersonic streams problem is notable in that the fluctuation splitting scheme exhibits superconvergent third-order spatial accuracy. For the inviscid cases of a supersonic diamond airfoil, supersonic slender cone, and incompressible circular bump the fluctuation splitting drag coefficient errors are typically half the DMFDSFV drag errors. However, for the incompressible inviscid sphere the fluctuation splitting drag error is larger than for DMFDSFV. A Blasius flat plate viscous validation case reveals a more accurate v-velocity profile for fluctuation splitting, and the reduced artificial dissipation production is shown relative to DMFDSFV. Remarkably the fluctuation splitting scheme shows grid converged skin friction coefficients with only five points in the boundary layer for this case. A viscous Mach 17.6 (perfect gas) cylinder case demonstrates solution monotonicity and heat transfer capability with the fluctuation splitting scheme. While fluctuation splitting is recommended over DMFDSFV, the difference in performance between the schemes is not so great as to obsolete DMFDSFV. The second half of the dissertation develops a local, compact, anisotropic unstructured mesh adaption scheme in conjunction with the multi-dimensional upwind solver, exhibiting a characteristic alignment behavior for scalar problems. This alignment behavior stands in contrast to the curvature clustering nature of the local, anisotropic unstructured adaption strategy based upon a posteriori error estimation that is used for comparison. The characteristic alignment is most pronounced for linear advection, with reduced improvement seen for the more complex non-linear advection and advection-diffusion cases. The adaption strategy is extended to the two-dimensional and axisymmetric Navier-Stokes equations of motion through the concept of fluctuation minimization. The system test case for the adaption strategy is a sting mounted capsule at Mach-10 wind tunnel conditions, considered in both two-dimensional and axisymmetric configurations. For this complex flowfield the adaption results are disappointing since feature alignment does not emerge from the local operations. Aggressive adaption is shown to result in a loss of robustness for the solver, particularly in the bow shock/stagnation point interaction region. Reducing the adaption strength maintains solution robustness but fails to produce significant improvement in the surface heat transfer predictions.
机译：针对非结构网格上的Navier-Stokes方程的二维和轴对称公式，开发并实施了多维迎风涨落分裂方案。该方案的关键特征是紧凑的模板，完全上卷和非线性离散化，可实现具有强制性的二阶精度。整个过程中，将波动分裂方案与当前最新的有限体积方法，二阶双网格迎风通量差异分裂方案（DMFDSFV）进行了比较，并显示了使用较少的计算机资源即可获得更准确的结果适用于各种测试案例。标量测试案例包括对流剪切，圆形对流，带有聚结冲击和膨胀风扇的非线性对流以及对流扩散。对于所有标量情况，波动拆分方案都更加精确，并且相对于DMFDSFV，提高波动拆分性能的主要机制是减少人工耗散的产生。最显着的标量结果是组合对流扩散，其中当前的波动分裂方案能够在比DMFDSFV更粗糙的网格上解决人工耗散的物理耗散，从而缩短求解时间的数量级。 。在无粘性的测试案例中，收敛的超音速流问题是显着的，因为波动分裂方案表现出超收敛的三阶空间精度。对于超音速金刚石翼型，超音速细长圆锥体和不可压缩的圆形凸块的无粘性情况，波动分裂阻力系数误差通常是DMFDSFV阻力误差的一半。但是，对于不可压缩的无粘性球，波动分裂阻力误差比DMFDSFV大。 Blasius平板粘性验证案例显示了更准确的 v -速度分布，用于波动分裂，并且相对于DMFDSFV而言，显示出减少的人工耗散量。值得注意的是，在这种情况下，波动分裂方案显示了边界层中只有五个点的网格收敛皮肤摩擦系数。粘稠的17.6马赫（完美气体）气缸壳通过波动分离方案展示了溶液的单调性和传热能力。尽管建议在DMFDSFV上使用波动分割，但这些方案之间的性能差异并不大，以致于过时的DMFDSFV。论文的后半部分结合多维迎风求解器，开发了一种局部的，紧凑的，各向异性的非结构化网格自适应方案，表现出标量问题的特征对准行为。这种对准行为与基于用于比较的后验误差估计的局部各向异性非结构化适应策略的曲率聚类性质形成对比。对于线性对流，特征对准最明显，对于更复杂的非线性对流和对流扩散情况，则减小了。通过最小化波动的概念，将自适应策略扩展到二维和轴对称的Navier-Stokes运动方程。适应策略的系统测试用例是在Mach-10风洞条件下安装在弦上的胶囊，在二维和轴对称配置中均考虑到。对于这种复杂的流场，适配结果令人失望，因为特征对齐不会从本地操作中出现。激进的适应被证明会导致求解器的鲁棒性下降，尤其是在船首冲击/停滞点相互作用区域。降低适应强度可保持解决方案的鲁棒性，但无法在表面传热预测中产生显着改善。

著录项

  • 作者

    Wood, William Alfred, III.;

  • 作者单位

    Virginia Polytechnic Institute and State University.;

  • 授予单位 Virginia Polytechnic Institute and State University.;
  • 学科 Engineering Aerospace.
  • 学位 Ph.D.
  • 年度 2001
  • 页码 378 p.
  • 总页数 378
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 航空、航天技术的研究与探索;
  • 关键词

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