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1D-Euler solver


packageEuler1D package contains a Godunov solver for 1D Euler equations.
Download packageEuler1D here .
The zip folder contains 3 folders:

  • codes
  • course
  • Doc
The folder codes contains the Fortran code, 3 text files for the input data, and 2 pdf files for a short desritpion of the code. These files:
  • main.f90
  • Fortran program
  • Text file that contains most of the command values (number of cells, timestep).
  • Text file that contains samples for initital conditions.
  • air_gaz.inp
  • Text file that contains values for the Equation of State (here, perfect gas).
  • CODE.pdf
  • pdf file that contains a short description of the code structure.
  • Principales_variables.pdf
  • pdf file that contains the list of the main variables.
1D-EULER computes unsteady solutions for Euler's equations. This is a FORTRAN code tested on linux with : GNU Fortran 7.4.0 (obutu 18.04.01)


This is a free software: you can redistribute, modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version. This code is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details available at the following address: GPL license. Everyone is permitted to copy and distribute verbatim copies of this license document, but changing it is not allowed.

Using and Warning

Code-Mφ disclaims any responsibility in the obtained results with the downloaded codes.
You are encouraged to signal errors, suggest improvements to the Code-Mφ team that will try to answer.

This code is a part of the universitary program of Polytech Marseille (Master degree and diplôme d'Ingénieurs at Aix-Marseille Université). For the students, this code is a necessary tool to extend the code to a 2D version.

Physical Model

Euler's equations represent the dynamics of an invsicid compressible fluid. An equation of state is required as a closure relation, here the perfect gas law.

Numerical scheme

This is 1D solver using regular or non-regular mesh spacing. The time integration is explicit. The global accuracy is 1rst order. The fluxes are computed thanks to an HLLC Riemann solver for the gas phase. This is a sequential program (run with 1 CPU).

Requirements and Installation

A Fortran compiler is required. Results can be easily plotted with Gnuplot (See

Compile and run

With gfortran compiler:

  • @myfolder:> gfortran -o main main.f90
  • @myfolder:> ./main