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UnDiFi-2D , an open source (free software) Un structured-grid, Di scontinuity Fi tting code, is presented. The aim of UnDiFi-2D is to model gas-dynamic discontinuities in two-dimensional (2D) flows as if they were true discontinuities of null thickness that bound regions of the flow-field where a smooth solution to the governing PDEs exists. UnDiFi-2D therefore needs to be coupled with an unstructured CFD solver that is used to discretize the governing PDEs within the smooth regions of the flow-field. Two different, in-house developed, CFD solvers are also included in the current distribution. The main features of the UnDiFi-2D software can be summarized as follows: Programming language UnDiFi-2D is written in standard Fortran 77/95; its design is highly modular in order to enhance simplicity of use, maintenance and allow coupling with virtually any existing CFD solver; Usability, maintenance and enhancement In order to improve the usability, maintenance and enhancement of the code also the documentation has been carefully taken into account. The git distributed versioning system has been adopted to facilitate collaborative maintenance and code development; Copyrights UnDiFi-2D is a free software that anyone can use, copy, distribute, change and improve under the GNU Public License version 3. The present paper is a manifesto of the first public release of the UnDiFi-2D code. It describes the currently implemented features, which are the result of more than a decade of still ongoing CFD developments. This work is focused on the computational techniques adopted and a detailed description of the main characteristics is reported. UnDiFi-2D capabilities are demonstrated by means of examples test cases. The design of the code allows to easily include existing CFD codes and is aimed at ease code reuse and readability. Program title: UnDiFi-2D CPC Library link to program files: https://doi.org/10.17632/5hwssmc2mx.1 Licensing provisions: GNU General Public License, version 3 Programming language: Fortran; developed and tested with Intel Fortran Compiler v. 18.0.3 and GNU gfortran. External routines: The code depends on several libraries and third-party packages which are detailed in the corpus of the text. Nature of problem: Numerical computation of flows with discontinuities. Solution method: Shock-fitting technique. Additional comments including restrictions and unusual features: • At present, UnDiFi-2D is validated for inviscid steady and unsteady two-dimensional flows without changes in the number of discontinuity lines and interaction points. • UnDiFi-2D implements a shock-fitting algorithm and can be coupled with unstructured cell-vertex solvers, with an Arbitrary Lagrangian-Eulerian (ALE) formulation. • UnDiFi-2D project adopts git [1], a free and open source distributed version control system. A public repository dedicated to UnDiFi-2D project [2] has been created on github [3], a web-based hosting service for software development projects using git versioning system. Finally, a comprehensive documentation is provided in the form of user manual developed in Pandoc [4]. [1] Git, a free and open source distributed version control system, http://git-scm.com. [2] UnDiFi-2D documentation, https://github.com/UnDiFi/UnDiFi-2D. [3] Github, a web-based hosting service for software development projects using git versioning system, https://github.com. [4] M. Dominici, TUGboat 35(1) (2014) 44-50. [ABSTRACT FROM AUTHOR]