Comparison of Explicit Method of Solution for CFD Euler Problems using MATLAB® and FORTRAN 77

Abstract

This work presents a comparison of an explicit method of solution for an inviscid compressible fluid mechanics problem using Euler equations for two-dimensional internal flows. The same algorithm was implemented in both FORTRAN 77 and MATLAB®. The algorithm includes Runge‒Kutta time marching scheme with smoothing. Both solvers were initialized in the same manner. In addition, it was ensured that both solvers have the exact same values for time step, convergence criteria, boundary conditions, and the grid. The only difference between the two solvers was the precision of variables. The problem solved was a two-dimensional dual bump with an accelerating flow through a duct. The same algorithm solving the Euler equations of fluid flow is implemented in both FORTRAN 77 and MATLAB®, and applied to identical input. While the solutions look qualitativly the same, a 20% difference in the stationary solution is observed. No claim is made of the relevance of the computations to actual fluid flow, rather the key takeaway being that two finite and deterministic computations of the same algorithm on the same input in FORTRAN 77 and MATLAB® produce different output.