Method of adaptive artificial viscosity for solving the Navier–Stokes equations
Tóm tắt
A numerical technique based on the method of adaptive artificial viscosity is proposed for solving the viscous compressible Navier–Stokes equations in two dimensions. The Navier–Stokes equations is approximated on unstructured meshes, namely, on triangular or tetrahedral elements. The monotonicity of the difference scheme according to the Friedrichs criterion is achieved by adding terms with adaptive artificial viscosity to the scheme. The adaptive artificial viscosity is determined by satisfying the maximum principle conditions. An external flow around a cylinder at various Reynolds numbers is computed as a numerical experiment.
Tài liệu tham khảo
I. V. Popov and I. V. Fryazinov, “Finite-difference method for solving gas dynamics equations using adaptive artificial viscosity,” Math. Models Comput. Simul. 1 (4), 493–502 (2009).
I. V. Popov and I. V. Fryazinov, “Adaptive artificial viscosity for multidimensional gas dynamics for Euler variables in Cartesian coordinates,” Math. Models Comput. Simul. 2 (4), 429–442 (2010).
I. V. Popov and I. V. Fryazinov, “Method of adaptive artificial viscosity for gas dynamics equations on triangular and tetrahedral grids,” Math. Models Comput. Simul. 5 (1), 50–62 (2013).
I. V. Popov and I. V. Fryazinov, Method of Adaptive Artificial Viscosity for the Numerical Solution of Gas Dynamics Equations (KRASAND, Moscow, 2014) [in Russian].
I. V. Popov and I. V. Fryazinov, “Finite-difference method for solving two-dimensional Navier–Stokes equations with adaptive artificial viscosity,” in Proceedings of the 10th International Conference on Grid Methods for Boundary Value Problems and Applications (Kazan. Univ., Kazan, 2014), pp. 503–509.