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The Finite Volume Method in Computational Fluid Dynamics to numerically modela fluid flow problem involves the process of formulating the numerical flux atthe faces of the control volume. This process is important in deciding theresolution of the numerical solution, thus its quality. In the current work,the performance of different flux construction methods when solving theone-dimensional Euler equations for an inviscid flow is analyzed through a testproblem in the literature having an exact (analytical) solution, which is theSod problem. The work considered twenty two flux methods, which are: exactRiemann solver (Godunov), Roe, Kurganov-Noelle-Petrova, Kurganov-Tadmor,Steger-Warming Flux Vector Splitting, van Leer Flux Vector Splitting, AUSM,AUSM+, AUSM+-up, AUFS, five variants of the Harten-Lax-van Leer (HLL) family,and their corresponding five variants of the Harten-Lax-van Leer-Contact (HLLC)family, Lax-Friedrichs (Lax), and Rusanov. The methods of exact Riemann solverand van Leer showed excellent performance. The Riemann exact method took thelongest runtime, but there was no significant difference in the runtime amongall methods.

The Sod gasdynamics problem as a tool for benchmarking face flux construction in the finite volume method