Using matrices in post-processing phase of CFD simulations
Gianluca Argentini
TL;DR
The paper tackles the high computational burden of post-processing CFD tracer trajectories by introducing a cubic-spline interpolation framework that blends a Bezier curve with a cubic spline between groups of four points, controlled via $v_k = \alpha b + \beta u_k$ with $\alpha=\beta=0.5$. Coefficients are obtained from a constant $4\times5$ matrix $T$ as $coeff = T p$, enabling a compact matrix formulation, while a sparse global matrix $G$ facilitates parallel evaluation across many trajectories. The approach achieves quasi-linear speedups on both MPI-based Linux clusters and MATLAB-based Windows clusters, leveraging sparsity ($G$ density ~ $1/M$) and a fixed matrix $T$ cached for performance. The work demonstrates substantial improvements in the post-processing phase of CFD simulations, with plans to extend to a global matrix product to further exploit sparsity and reduce memory usage. The practical impact is faster, scalable rendering of high-resolution particle trajectories for industrial burner design and optimization.
Abstract
In this work 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 I have used a parallel environment using a multiprocessor cluster architecture. The efficiency of the used method is good, mainly reducing the number of floating-points computations by caching the numerical values of some line-parameter's powers, and reducing the necessity of communication among processes. This work has been developed for the Research and Development Department of my company for planning advanced customized models of industrial burners.