论文标题
圆周靠近湍流速度场的分数PDE模型
A fractional PDE model for turbulent velocity fields near solid walls
论文作者
论文摘要
本文介绍了一类用随机载荷的分数偏微分方程（FPDE）编写的湍流模型。这些FPDE模型的每种解决方案都是不可压缩的速度场，解决方案的分布都是高斯。湍流与固体壁的相互作用是通过实施各种边界条件的。各种边界条件在可以建模的近壁统计数据中具有广泛的灵活性。重现了完全发达的无剪切和均匀剪切边界层湍流，这是两个简单的物理应用。第一个也可以通过实验数据直接验证。不均匀的合成湍流入口边界条件的渲染是由当代数值风洞模拟的促进的附加应用。还授予模型参数和有效数值方法的校准。
This paper presents a class of turbulence models written in terms of fractional partial differential equations (FPDEs) with stochastic loads. Every solution of these FPDE models is an incompressible velocity field and the distribution of solutions is Gaussian. Interaction of the turbulence with solid walls is incorporated through the enforcement of various boundary conditions. The various boundary conditions deliver extensive flexibility in the near-wall statistics that can be modelled. Reproduction of both fully-developed shear-free and uniform shear boundary layer turbulence are highlighted as two simple physical applications; the first of which is also directly validated with experimental data. The rendering of inhomogeneous synthetic turbulence inlet boundary conditions is an additional application, motivated by contemporary numerical wind tunnel simulations. Calibration of model parameters and efficient numerical methods are also conferred upon.
