ARTIFICIAL VISCOSITY IN THE GODUNOV’S-TYPE SCHEMES AS THE METHOD OF "CARBUNCLE"-INSTABILITY SUPRESSION
A. V. Rodionov, I. Yu. Tagirova
VANT. Ser.: Mat. Mod. Fiz. Proc 2015. Вып.2. С. 3-11.
The paper describes a new method of solving the "carbuncle"-problem, its essence is the introduction of dissipative dopants in the form of right-hand parts of the Navier-Stokes equations, where the molecular viscosity is replaced by the artificial one (i.e. the tensor of artificial viscous tension is introduced). Artificial viscosity is the second infinitesimal order quantity which, like in the artificial Neumann-Richtmyer viscosity, is proportional to the velocity divergence. The principle difference here is the limiter, which prevents the additional dissipation out of the front of an intense shock. The new method of solving the carbuncle-problem, being the external relative to a certain scheme, does not change the algorithm of the non-viscous flow simulation. The efficiency of the proposed approach is proved by the examples of solving several test problems: the Kirk problem (broken one-dimensionality of a plane shock wave), strong shock diffraction on the right angle and the "Double Mach Reflection". Keywords: hypersonic flows, Euler and Navier-Stokes equations, carbuncle-problem, Godunov’s-type schemes, artificial viscosity.
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