Where can I find manufactured solutions for the 2d Euler equations, with the complete analytical terms, including the Jacobian of the source term ?

  • $\begingroup$ Welcome to SciComp.SE! The point of manufactured solutions is that you can easily make your own, so it's not quite clear what you're asking for here. You can find analytical (and presumably physical) solutions to Euler's equations in sciencedirect.com/science/article/pii/S0895717703901105 $\endgroup$ Oct 27, 2015 at 11:00
  • $\begingroup$ I was looking if possible for something more directly implementable, like the analytical expressions of the solutions, their analytical source terms, and the derivatives of the source terms. $\endgroup$
    – Gonzague
    Oct 27, 2015 at 11:10
  • $\begingroup$ You just repeated what you wrote in the question. $\endgroup$
    – nicoguaro
    Oct 27, 2015 at 22:35

2 Answers 2


This 2004 paper by Roy et. al in Int. J. Numer. Meth. Fluids 2004; 44:599–620 (DOI: 10.1002/d.660) should contain exactly what you're looking for:


You can contact the authors to obtain a copy of the FORTRAN code for the source terms (and their derivatives), or generate them yourself using symbolic manipulation software such as Mathematica.

Another paper by the same authors:



You can find information about Manufactured solutions in this repository. Particularly,

Malaya, Nicholas, et al. "MASA: a library for verification using manufactured and analytical solutions." Engineering with Computers 29.4 (2013): 487-496.

That have the codes in this GitHub repository.

MASA (Manufactured Analytical Solution Abstraction) is a library written in C++ (with C, python and Fortran90 interfaces) which provides a suite of manufactured solutions for the software verification of partial differential equation solvers in multiple dimensions. Example formulations include:

Heat Equation
Laplace's Equation
Euler Equations (with and without thermal equilibrium chemistry)
Navier-Stokes Equations
Reynolds Averaged Navier Stokes with Various Turbulence Models


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