Effects of visualization using different convolution kernels in Julia

Abstract: Many real-world engineering problems require large amounts of data in order to accurately model and predict outcomes. However, this data is often noisy, sampled and discontinuous, making the data difficult to process and giving rise to incorrect models. In order to address this issue, different interpolation techniques are commonly used to make the data continuous. This can then followed by a filtering process in order to reduce noise and further reduce discontinuities. In this report, our approach to filtering is the use of convolution kernels, which smooths out the data. By doing so, a better visual representation of the limited data available can be obtained. For instance, in the specific case of studying streamlines and vortices, filtering techniques have been used to produce more realistic plots. While the use of filters can be beneficial, it is important to note that the choice of filter and its parameters can greatly impact the results obtained. In particular, we found that, for the filters we studied, applying these to analytical functions can actually increase the error. On the other hand, when filters are applied to discontinuous functions, they can improve the accuracy of the data. Overall, when analyzing stream functions with filters, significant improvements can be seen in the quality of the data. This underscores the importance of careful selection and application of filtering techniques in engineering problems that involve large amounts of noisy and discontinuous data.