50 Years of CFD in Engineering Sciences - A Commemorative Volume in Memory of D. Brian Spalding
50 Years of CFD in Engineering Sciences - A Commemorative Volume in Memory of D. Brian Spalding
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工程科学 CFD 50 周年 - 纪念 D. Brian Spalding 的纪念卷
DOI：
10.1007/978-981-15-2670-1_20
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发表时间：
2020
期刊：
影响因子：
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通讯作者：
Cotta R
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作者：
Cotta R
广义积分变换技术（GITT）的审查作为一种混合的数值分析方法的线性或非线性扩散和对流扩散偏微分方程，包括一类重要的共轭问题的传热和流体流动分析。这一章的重点是处理不规则区域和异构域，作为对D。B。早在1994年，斯伯丁就在与第一作者的一次私人交流中激发了这一研究方向。首先，非线性扩散和对流扩散公式的正式解决方案进行审查，包括采用非线性和/或对流特征值问题的替代方案，无论是全部或部分转换计划。接下来，GITT本身是正式的线性和非线性特征值问题的解决方案，包括直接积分变换的问题定义在不规则域，基于更简单的辅助特征值问题写相同的几何形状。然后，讨论了一个单一的域重构策略，它占的非均匀性的物理性质或几何形式，通过重写不同的介质转换为空间变量方程系数和源项。这两个互补的策略，然后通过对流和共轭传导对流问题的代表性例子说明，确认所提出的本征函数展开的优良收敛特性，对建立基准参考结果集。目前的混合解决方案也共同验证纯数值通用CFD代码的结果。
The Generalized Integral Transform Technique (GITT) is reviewed as a hybrid numerical–analytical approach for linear or nonlinear diffusive and convective–diffusive partial differential formulations, including an important class of conjugated problems in heat transfer and fluid flow analyses. This chapter focus is on the handling of irregular regions and heterogeneous domains, as a tribute to Prof. D. B. Spalding, who stimulated this research direction in a private communication with the first author, back in 1994. First, formal solutions for nonlinear diffusion and convection–diffusion formulations are reviewed, including the alternatives of adopting nonlinear and/or convective eigenvalue problems, either on total or partial transformation schemes. Next, the GITT itself is formalized in the solution of linear and nonlinear eigenvalue problems, including the direct integral transformation of problems defined in irregular domains, based on simpler auxiliary eigenvalue problems written for the same geometry. Then, a single domain reformulation strategy is discussed, which accounts for heterogeneities on either physical properties or geometrical forms, by rewriting the different media transitions as space variable equation coefficients and source terms. The two complementary strategies are then illustrated through representative examples in convection and conjugated conduction–convection problems, confirming the excellent convergence characteristics of the proposed eigenfunction expansions, toward the establishment of sets of benchmark reference results. The present hybrid solutions are also co-verified against results from purely numerical general-purpose CFD codes.