“Nesvetay” is a Fortran-90 library of codes, which realize modern Godunov-type methods to solve various two- and three-dimensional equations of fluid motion in arbitrary domains. The key idea is to share the key elements such as mesh handling, advection schemes and parallelization across various solvers. At present, the software solves compressible Euler and multiphase equations as well as the Boltzmann kinetic equations with various model collision integrals: BGK, S-model of E. M. Shakhov, R-model of V. A. Rykov.

       The library has been under development by Dr Titarev since 2006 and consists of two parts.

       “Nesvetay-2D” contains modules to solve linear advection equations, compressible Euler equations as well as various model kinetic equations on mixed-element unstructured meshes in two space dimensions.

       Main features include:

• Use of arbitrary triangular and quadrilateral meshes, imported in Gambit’s “neutral” file format
• A variety of modern Godunov-type methods for advection part, including TVD methods and WENO-type methods
• One-step implicit type evolution for kinetic equations
• Efficient OpenMP & MPI parallelization for the kinetic solver.

       “Nesvetay-3D” contains modules to solve linear advection equations, compressible Euler equations as well as various model kinetic equations (BGK, Shakhov, Rykov models) on mixed-element unstructured meshes in three space dimensions.

       Main features include:

• Use of arbitrary mixed element meshes, including tetrahedral, prismatic, hexahedral and pyramidal shapes
• Support of Gambit’s “neutral” and StarCD file formats
• A variety of modern Godunov-type methods for advection part, including TVD methods and WENO-type methods
• Support of rotating frame of reference for compressible Euler equations
• One-step implicit time evolution for model kinetic equations
• OpenMP parallelization for all solvers
• Efficient MPI parallelization in velocity space for the kinetic solver, excellent scalability up to 512 cores
• Domain-decomposition type MPI parallelization for all solvers.

       The implemented kinetic solver offers the following advantages over the existing state-of-the art methods and codes:

• The use of unstructured meshes in physical space simplifies the complex geometries and allows for efficient and accurate resolution of near-wall layers.
• TVD advection scheme works well for both large Knudsen numbers, when discontinuities of distribution function play an important role, and for moderate and small Knudsen numbers, for which the high order of accuracy is important.
• The one-step implicit time discretization method accelerates convergence to a steady state by at least an order of magnitude as compared with explicit time evolution methods.
• Good scalability of the method makes it possible to use relatively fine meshes with moderate computational time required.

       Key publications:

1. V. Titarev, M. Dumbser and S. Utyuzhnikov. Construction and comparison of parallel implicit kinetic solvers in three spatial dimensions // J. Comp. Phys. 2014. V. 256, p. 17-33.
2. V.A. Titarev, Direct numerical solution of model kinetic equations for flows in arbitrary three-dimensional geometries // Rarefied Gas Dynamics. 2012. Proc. 28th Int. Symp., AIP Conf. Proc. 1501, p. 262-271.
3. V. A. Titarev and E. M. Shakhov. Computational study of a rarefied gas flow through a long circular pipe into vacuum // Vacuum, Special Issue ``Vacuum Gas Dynamics'', 2012. V. 81, N. 11, p. 1709-1716.
4. V. A. Titarev. Efficient deterministic modelling of three-dimensional rarefied gas flows // Communications in Computational Physics. 2012. V. 12, , N 1 pp. 162-192.
5. P. Tsoutsanis, V. A. Titarev and D. Drikakis. WENO schemes on arbitrary mixed-element unstructured meshes in three space dimensions // Journal of Computational Physics, 2011. V. 230, pp. 1585 – 1601.
6. V. A. Titarev. Implicit unstructured-mesh method for calculating Poiseuille flows of rarefied gas // Communications in Computational Physics. 2010. V. 8, No. 2, pp. 427 – 444.
7. M. Dumbser, M. Käser, V. A. Titarev and E. F. Toro. Quadrature-free non-oscillatory finite volume schemes on unstructured meshes for nonlinear hyperbolic systems // Journal of Computational Physics. 2007. V. 221, No. 2, pp. 693 – 723.
8. V. A. Titarev. Conservative numerical methods for model kinetic equations // Computers and Fluids, 2007. V. 36, No. 9, pp. 1446 – 1459.