Modified characteristics mixed defect-correction finite element method for the time-dependent Navier–Stokes problems

Abstract

In this paper, a modified method of characteristics mixed defect-correction finite element method (MMOCMDCFEM) for the time-dependent Navier-Stokes problems, which is led by combining the characteristics time discretization with the two-step defect-correction in space, is presented. In this method, the hyperbolic part (the temporal and advection term) are treated by a characteristic tracking scheme. Then, we solve the equations with an added artificial viscosity term and correct these solutions by using a defect-correction technique. The theory analysis shows that this method has a good convergence property. In order to show the efficiency of the MMOCMDCFEM, we first present some numerical results of analytical solution problems. Then, we give some numerical results of lid-driven cavity flow with Re = 5000 and 7500. We also give some numerical results of flow around a cylinder problems, and compare the results with MMOCFEM's. The numerical results show that this method is highly Efficient.

Characteristic stabilized finite element method for non-stationary conduction-convection problems

“…Lemma 3.4 (Si et al , 2015). Let e(x,m)=[um(x)−trueu¯m−1(x)Δt−Dtum(x)] and let Δ t > 0 be such that u∈scriptC4([Δt,t*];H3(Ω)2) .…”

“…For the convection-dominated problems, the characteristic method is an efficient method (Douglas and Russell, 1982; Süli, 1988; Pironneau, 1982; Russell, 1985; Si et al , 2015; Si, 2012; Si et al , 2014). This method is based on the discretization of the material derivative term (i.e.…”

Modified Method of Characteristics Variational Multiscale Finite Element Method for Time Dependent Navier-Stokes Problems

“…An optimal error estimate for the Lagrange-Galerkin mixed finite element approximation of the Navier-Stokes equations was given by Süli in [43]. In [38,39], one order and second order MMOC mixed defect-correction finite element methods for timedependent Navier-Stokes problems were given. In [41], second order in time MMOC variational multiscale finite element method for the time-dependent Navier-Stokes equation was shown.…”

A semi‐discrete defect correction finite element method for unsteady incompressible magnetohydrodynamics equations

“…In , we give the defect correction finite element method for the conduction‐convection problems. We also give the defect correction method combined with modified characteristics method for time‐dependent Navier–Stokes equations . In , we gave a defect correction finite element method for the stationary MHD equations.…”