Building a Bridge from Moments to PDF's: A New Approach to Finding PDF Mixing Models

TL;DR

This paper introduces a novel approach to develop and transfer an improved mixing model from concentration variance to probability density functions, enhancing the accuracy of groundwater solute transport predictions under uncertainty.

Contribution

It presents a new method to derive and validate a mixing model for both concentration variance and PDF equations, improving modeling accuracy.

Findings

Significantly improved variance modeling results.

Enhanced PDF modeling accuracy.

Validated transferability of the mixing model.

Abstract

Probability density function (PDF) methods are a promising alternative to predicting the transport of solutes in groundwater under uncertainty. They make it possible to derive the evolution equations of the mean concentration and the concentration variance, used in moment methods. A mixing model, also known as a dissipation model, is essential for both methods. Finding a satisfactory mixing model is still an open question and due to the rather elaborate PDF methods, a difficult undertaking. Both the PDF equation and the concentration variance equation depend on the same mixing model. This connection is used to find and test an improved mixing model for the much easier to handle concentration variance. Subsequently, this mixing model is transferred to the PDF equation and tested. The newly proposed mixing model yields significantly improved results for both variance modelling and PDF modelling.