hllc riemann solver
The Harten-Lax-van Leer-Contact (HLLC) approximate Riemann solver is an
extension of the HLL (Harten, Lax, and van Leer) solver (Harten et al., 1983) by
Toro et al. (1994). In the original HLL Riemann approximation, the presence of
contact discontinuities is neglected, which can result in errors in the presence of
shears within the flow. In Toro's extension (HLLC), the contact and shear waves are
restored in the solution of the Riemann problem and it has the following three
properties (Luo et al., 2003):
1. Ability to resolve contact discontinuities and shear waves.
2. Positivity preservation of scalar quantities.
3. Enforcement of the entropy condition.
In this study the HLLC solver was implemented for Navier-Stokes Equations
governing atmospheric flows on unstructured adaptive grids.
convection in neutral atmosphere
details
Harten, A., P. Lax, and B. van Leer, 1983: On upstream differencing and Godunov-type schemes for
hyperbolic conservation laws, SIAM Rev., 25, 35-61.
Toro, E. F., M. Spruce, and W. Speares, 1994: Restoration of the Contact Surface in the HLL Riemann
Solver, Shock Waves, 4, 25-34.
Luo, H., J. D. Baum, and R. Lohner, 2003: Extension of HLLC Scheme for Flows at all Speeds.
American Institute of Aeronautics and Astronautics. AIAA Paper 2003-3840.
Ahmad, N., Z. Boybeyi, R. Lohner and A. Sarma,
2007: A
Godunov-Type Scheme for Atmospheric Flows on Unstructured Grids:
Euler and Navier-Stokes Equations.
Pure and Applied Geophysics, 164:1, 217-244.