Session: Flow Visualization and Regular Poster Session

Paper Number: 156121

156121 - Clustering and Classification Techniques for Improved Flux Calculations 

Abstract: 

Various mathematical mechanisms exist for approximating spatial derivatives in solution of partial differential equations (PDEs). Finite difference (FD) approaches assume a piecewise linear relationship between neighboring points. FD is an ideal starting place, due to its simplicity in concept and application, however, this naive approximation struggles to return stable solutions in even the simplest PDEs. High order FD schemes are available, and demonstrate accuracy and stability, however at greater cost.

In this paper machine learning techniques are used to choose the between FD approaches to solving for spatial derivatives in the advection transport equation for fluid flow. Three approaches are examined. First clustering techniques are applied to the solution values. Using the solution values as the feature set, clusters are formed and regression models for each cluster are developed for the flux approximation. Two clustering techniques are examined, Kmeans and Gaussian Mixture models. Secondly, a classification approach is used. The data set is manually labeled, and machine learning classification techniques are applied, with the expectation that training a smaller more similar subset with result in better performing regression models. Thirdly, two regression techniques are explored for returning the optimal flux approximation.

The study is limited to five-point approximations for the spatial derivatives. All the training data for this paper is generated using automatic differentiation. The data is specifically modeled to solve the 1D transient advection equation with a source term, leveraging the PDE to improve the Machine learning models.

These approaches are implimented toward the solution of a one-dimensional fluid flow containing a shock. Shocks are difficult to capture, as the sudden high gradients cause information from either side of the shock to ripple outward. This method will work to dampen the oscillations so frequently found in finite difference models.

Presenting Author: Amandine Maidenberg Embry-Riddle Aeronautical University

Presenting Author Biography: