Stochastic Backscatter Model for Unstructured Solvers

TL;DR

This paper introduces a stochastic backscatter model designed for unstructured solvers in computational fluid dynamics, focusing on deriving the spatial correlation analytically when using implicit Laplace smoothing.

Contribution

It extends the stochastic backscatter model to unstructured solvers by analytically deriving the spatial correlation with Laplace smoothing.

Findings

The model generates correlated random variables suitable for unstructured CFD solvers.

Analytical derivation of spatial correlation for Laplace smoothing is provided.

The approach broadens the applicability of stochastic backscatter models in CFD simulations.

Abstract

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.