GodunovSPH

GodunovSPH is a Computational Fluid Dynamics library for modelling compressible flows in physics and engineering. In particular, it enables numerical experimentation in aeronautics, astronautics and astrophysics.

It is based on a Generalised Riemann Problem quasi-conservative scheme, of Ben-Artzi and Falcovitz, as an extension of Godunov's Finite Volume Solver for discontinuity capturing.

It also enables astrophysical modelling via a Smoothed Particle Hydrodynamics code, which makes use of the GRP solver to capture hyperbolic effects.

Code

• The core solver routines are written in object-oriented C++

Completed

• Create RiemannSolverEulerBase abstract base class to be inherited by all subsequent Riemann solver objects, based on Euler equations of gas dynamics
• Create an exact Riemann solver (RiemannSolverEulerExact) for the one-dimensional Euler equations based on Chapter 4 of [1], providing a testing capability

Roadmap

• Create a second order (space/time) Godunov-type conservative scheme solver for the 1D Euler equations using the Generalised Riemann Problem method of Ben-Artzi and Falcovitz [2]
• Extend the 1D GRP-based Godunov solver to multiple dimensions on Cartesian structured geometries, based on the operator splitting techniques of Strang
• Extend the GRP-based Godunov solver to unstructured meshes, including a variety of test problems
• Create a smoothed particle hydrodynamics (SPH) code
• Add the GRP Riemann solver to the SPH code to handle flow discontinuities
• Apply the software to multiple test objects in aeronautics, astronautics and astrophysics

Extensions

• Create a Harten, Lax and van Leer Riemann solver (HLL) as well as Harten, Lax and van Leer with contact capability (via Toro); HLLC. Finally, create the HLLE solver (Einfeldt modification)
• Create a Riemann solver based on Roe's approximation, which will be useful when creating semi-homogeneous flow fields

References

[1] Riemann Solvers and Numerical Methods for Fluid Dynamics - A Practical Introduction, 2nd Edition, E.F. Toro [2] Generalized Riemann Problems in Computational Fluid Dynamics, M. Ben-Artzi and J. Falcovitz