Using sparse matrices and splines-based interpolation in computational fluid dynamics simulations

TL;DR

This paper introduces a method using sparse matrices and spline interpolation to efficiently smooth and render particle trajectories in fluid dynamics simulations, optimized for parallel computing environments.

Contribution

It presents a novel approach for interpolating 3D points with cubic splines and implementing it efficiently on multiprocessor clusters for fluid flow visualization.

Findings

Effective interpolation of 3D particle trajectories

Fast evaluation suitable for high-resolution rendering

Parallel implementation on multiprocessor clusters

Abstract

In this relation I present a technique of construction and fast evaluation of a family of cubic polynomials for analytic smoothing and graphical rendering of particles trajectories for flows in a generic geometry. The principal result of the work was implementation and test of a method for interpolating 3D points by regular parametric curves and their fast and efficient evaluation for a good resolution of rendering. For the purpose a parallel environment using a multiprocessor cluster architecture has been used. This work has been developed for the Research and Development Department of my company for planning advanced customized models of industrial burners.