Applications of Computational Mathematics to Simulation and Data Analysis: Two-dimensional Vortex Dynamics and Meteorological Data Reconstruction

Abstract

This research is developed within two main areas of Applied Computational Mathematics: Simulation and Data Analysis. In the simulation component, the study investigates the motion of a passive particle on a spherical surface under the influence of multiple point vortices. The aim is to find an energy-minimising trajectory that respects constraints such as specified departure and arrival points, as well as a fixed travel time. In the data analysis component, the research focuses on reconstructing incomplete meteorological time series by addressing gaps caused by missing records. The proposed methodology seeks to maximise the use of available information from predictor stations while ensuring both high accuracy and computational efficiency.