标题： 随机反散射模型用于非结构化求解器 显示英文标题

标题： Stochastic Backscatter Model for Unstructured Solvers

摘要： 随机反散射模型涉及生成一组由空间和时间中预定相关性表征的随机变量。 这些变量是通过平滑一个最初不相关的随机场得到的，这会产生指数衰减的空间相关性。 平滑操作是隐式地并在计算域的三个坐标方向上依次进行的，使得该方法仅适用于结构化CFD求解器。 为了将该方法扩展到非结构化求解器，可以改用隐式拉普拉斯平滑。 然而，这种替代方法产生的空间相关性必须通过解析方式推导得出。 这就是本论文的主要目标。 显示英文摘要

摘要： The Stochastic Backscatter Model involves the generation of a set of random variables characterised by prescribed correlations in space and time. These variables are obtained by smoothing an initially uncorrelated random field, which produces an exponentially decaying spatial correlation. The smoothing is applied implicitly and sequentially along the three coordinate directions of the computational domain, making the approach suitable only for structured CFD solvers. To extend the method to unstructured solvers, implicit Laplace smoothing can be employed instead. However, the spatial correlation resulting from this alternative approach must be derived analytically. This constitutes the main objective of the present dissertation.