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Genuinely nonlinear models for convection-dominated problems. (English) Zbl 1329.76173
Summary: This paper introduces a general, nonlinear subgrid-scale (SGS) model, having boundedartificial viscosity, for the numerical simulation of convection-dominated problems. We also present a numerical comparison (error analysis and numerical experiments) between this model and the most common SGS model of Smagorinsky, which uses a \(p\)-Laplacian regularization. The numerical experiments for the 2-D convection-dominated convection-diffusion test problem show a clear improvement in solution quality for the new SGS model. This improvement is consistent with the bounded amount of artificial viscosity introduced by the new SGS model in the sharp transition regions.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
74R99 Fracture and damage
76F02 Fundamentals of turbulence
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