Discretization Of Incompressible Navier-Stokes Equations Research Articles

Algebraic spectral analysis of the DSSR preconditioner

The dimension-wise splitting with selective relaxation (DSSR) is an efficient iterative method for solving linear systems arising from the discretization of incompressible Navier-Stokes equations. The unconditional convergence properties and optimal relaxation parameters are analyzed at the continuous level on model problems in Gander et al. (2016) [15] In this paper, we provide an algebraically spectral analysis of the DSSR preconditioner when applied to Krylov subspace methods. The analysis indicates that most eigenvalues of the preconditioned matrix are 1, and the corresponding eigenspace is nondeficient, which is an important favorable property for fast convergence of Krylov subspace iterative method. Finally, the preconditioner is explained from the deflation point of view, which provides a clue for developing hybrid direct iterative solvers.

Mean-Square Approximation of Navier-Stokes Equations with Additive Noise in Vorticity-Velocity Formulation

We consider a time discretization of incompressible Navier-Stokes equations with spatial periodic boundary conditions in the vorticity-velocity formulation. The approximation is based on freezing the velocity on time subintervals resulting in linear parabolic equations for vorticity. Probabilistic representations for solutions of these linear equations are given. At each time step, the velocity is expressed via vorticity using a formula corresponding to the Biot--Savart-type law. We show that the approximation is divergent free and of first order. The results are extended to two-dimensional stochastic Navier-Stokes equations with additive noise, where, in particular, we prove the first mean-square convergence order of the vorticity approximation.

Large-Eddy Simulation of Internal Flow through Human Vocal Folds

The phonatory process occurs when air is expelled from the lungs through the glottis and the pressure drop causes flow-induced oscillations of the vocal folds. The flow fields created in phonation are highly unsteady and the coherent vortex structures are also generated. For accuracy it is essential to compute on humanlike computational domain and appropriate mathematical model. The work deals with numerical simulation of air flow within the space between plicae vocales and plicae vestibulares. In addition to the dynamic width of the rima glottidis, where the sound is generated, there are lateral ventriculus laryngis and sacculus laryngis included in the computational domain as well. The paper presents the results from OpenFOAM which are obtained with a large-eddy simulation using second-order finite volume discretization of incompressible Navier-Stokes equations. Large-eddy simulations with different subgrid scale models are executed on structured mesh. In these cases are used only the subgrid scale models which model turbulence via turbulent viscosity and Boussinesq approximation in subglottal and supraglottal area in larynx.

Development of a Compact and Accurate Discretization for Incompressible Navier-Stokes Equations Based on an Equation-Solving Solution Gradient, Part III: Fluid Flow Simulations on Staggered Polygonal Grids

A compact and accuracy discretization of incompressible Navier-Stokes equations on staggered polygonal grids is presented in this article. It is a sequel to our efforts in developing a feasible solution procedure to simulate incompressible flow problems in complicated domains. By taking advantage of the discretization procedure for the convection-diffusion equation described in our previous work, difference counterparts of the Navier-Stokes equations can be obtained on staggered polygonal grids. Additional ingredients of pressure–velocity coupling and boundary conditions for velocity gradients in the solution procedure are also described. Several test problems are solved to illustrate the feasibility of the present formulation. From the numerical results obtained, it is evident that the proposed scheme is a useful tools to simulate incompressible flow field in arbitrary domains.