Benchmarking Modern Scientific Computing Platforms for 2D Potential Flow Solver

Abstract

We present a comprehensive performance analysis of three major scientific computing platforms-Python, Julia, and R-in solving two-dimensional potential flow around dual square obstacles. We implemented a numerical solution using the Jacobi iteration method across all three platforms, with careful consideration of boundary conditions and convergence criteria. The numerical implementation successfully demonstrated convergence with an L₂ norm reduction from 10⁰ to 10^-2 over 40,000 iterations, capturing fundamental flow physics including stagnation points (C_p ≅ 1), flow acceleration regions (C_p < 0), and obstacle interference effects. Through 200 independent executions and 10,000 bootstrap iterations, our comparative performance analysis revealed that Julia achieved superior computational efficiency with a median runtime of approximately 30 seconds, despite higher memory requirements (512MB), while Python offered balanced performance (45s, 108MB) and R showed higher variability in execution time (65s, 185MB). Statistical significance of these performance differences was confirmed through rigorous testing using Mann-Whitney U tests with Bonferroni correction (α_adjusted = 0.0167) and bootstrap resampling methods. The results provide valuable insights into the trade-offs between computational efficiency and resource utilization across modern scientific computing platforms, while also validating the numerical accuracy of our potential flow solver implementation. This benchmarking study contributes to the growing body of knowledge regarding platform selection for computational fluid dynamics applications, particularly in educational and rapid prototyping contexts.