CNSFVHLLCBase
CNSFVHLLCBase
is the base class from which all Harten-Lax-Van Leer-Contact (HLLC) residual computing objects inherit from. It computes the wave speeds for the HLLC formulation. Because it is the base class for all HLLC residual objects, we will use its documentation page to outline the HLLC equations. The HLLC flux is defined as:
where are the left and right evaluations respectively of the convective flux:
where where and is the normal vector at the face. , , and represent the , , and components of the normal vector respectively, while , , and represent the , , and components of the velocity respectively. is the static pressure and where is the specific internal energy. is the density. , , and are the left, middle, and right wave speeds respectively. is given by (Toro, 2009):
The intermediate flux states (denoted by *) are described by (Toro, 2009):
where the solution states are given by the left and right evaluations of
where and respectively and the intermediate solution states (the * states) are described by the left and right evaluations of (Toro, 2009):
The final piece to finish the definition of the HLLC flux is to specify the evaluation of the left and right wave speeds, and . These can be evaluated in a variety of ways, but the current CNSFVHLLCBase
implementation evaluates them as follows, following (Batten et al., 1997):
where denotes the local speed of sound in the medium and denotes Roe-averaged quantities which are computed via
where can be any quantity such as or .
References
- P Batten, MA Leschziner, and UC Goldberg.
Average-state Jacobians and implicit methods for compressible viscous and turbulent flows.
Journal of Computational Physics, 137(1):38–78, 1997.[BibTeX]
- Eleuterio F Toro.
Riemann solvers and numerical methods for fluid dynamics: a practical introduction.
Springer Science & Business Media, 3rd edition, 2009.[BibTeX]