ColESo: Collection of exact solutions for verification of numerical algorithms for simulation of compressible flows

Abstract

ColESo is a set of subroutines that evaluate particular solutions of the Euler equations, the Navier – Stokes equations, and their linearized versions. These solutions were used by the author for the verification of high-order methods for the compressible flow simulation. It is convenient to use an exact solution when it is available for each point of the computational domain, accurate enough, and quick to evaluate. A solution given by a composition of elementary functions is usually a good choice, but the set of such solutions is too limited. ColESo adds to this set several solutions in integral form and provides their quick calculation with a good accuracy. Program summaryProgram Title: ColESoCPC Library link to program files:https://doi.org/10.17632/z7mypchgfz.1Developer's repository link:https://github.com/bahvalo/ColESoCode Ocean capsule:https://codeocean.com/capsule/0365245Licensing provisions: GPLv2.1Programming language: C++ (C++03 standard)Nature of problem: Verification of high-order methods for the simulation of compressible gas dynamics on curvilinear or unstructured grids.Solution method: Change of variables, Fourier transformation, Gauss–Legendre and Gauss–Jacobi quadrature rules.Additional comments including restrictions and unusual features: ColESo uses several special functions provided by Cephes Math Library and GNU LibQuadMath (for the quadruple precision). To define the Gauss – Jacobi quadrature rules, ColESo uses a code written by S. Elhay, J. Kautsky, J. Burkadrt. These libraries are open-access and distributable with compatible licenses.