An entropy stable finite volume scheme for the two dimensional Navier-Stokes equations on triangular grids. (English) Zbl 1426.76414
Summary: We construct a finite volume scheme for the compressible Navier-Stokes equations on triangular grids which are entropy stable at the semi-discrete level. This is achieved by using entropy stable inviscid fluxes constructed in the recently published work [the first author et al., Commun. Comput. Phys. 19, No. 5, 1111–1140 (2016; Zbl 1373.76143)], and computing viscous fluxes in terms of entropy variables. Wall boundary conditions are also constructed to be entropy stable and are imposed in a weak manner. The resulting scheme is applied to solve several standard viscous test cases, such as flow over a flat-plat, flow past a NACA-0012 airfoil and unsteady flow past a cylinder, to demonstrate its stability and accuracy.
MSC:
| 76M12 | Finite volume methods applied to problems in fluid mechanics |
| 65M08 | Finite volume methods for initial value and initial-boundary value problems involving PDEs |
| 35Q30 | Navier-Stokes equations |
| 76N15 | Gas dynamics (general theory) |
Keywords:
Navier-Stokes equations; entropy stability; unstructured grid; finite volume scheme; wall boundary conditionCitations:
Zbl 1373.76143Software:
ChebfunReferences:
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