Second order modified method of characteristics mixed defect-correction finite element method for time dependent Navier-Stokes problems. (English) Zbl 1432.76084
Summary: In this paper, a second order modified method of characteristics defect-correction (SOMMOCDC) mixed finite element method for the time dependent Navier-Stokes problems is presented. In this method, the hyperbolic part (the temporal and advection term) are treated by a second order characteristics tracking scheme, and the non-linear term is linearized at the same time. Then, we solve the equations with an added artificial viscosity term and correct this solution by using the defect-correction technique. The error analysis shows that this method has a good convergence property. In order to show the efficiency of the SOMMOCDC mixed finite element method, we first present some numerical results of an analytical solution problem, which agrees very well with our theoretical results. Then, we give some numerical results of lid-driven cavity flow with the Reynolds number \(Re = 5,000\), \(7,500\) and \(10,000\). From these numerical results, we can see that the schemes can result in good accuracy, which shows that this method is highly efficient.
MSC:
| 76D05 | Navier-Stokes equations for incompressible viscous fluids |
| 76M10 | Finite element methods applied to problems in fluid mechanics |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 65M12 | Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs |
Keywords:
Second order modified method of characteristics; defect-correction finite element method; time-dependent Navier-Stokes problems; Error estimate; LID-driven problem; Incompressible flowReferences:
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