Article

# Preconditioning of the Euler and Navier-Stokes equations in low-velocity flow simulation on unstructured grids

Computational Mathematics and Mathematical Physics (Impact Factor: 0.79). 10/2009; 49(10):1789-1804. DOI: 10.1134/S0965542509100133

**ABSTRACT**

Low-velocity inviscid and viscous flows are simulated using the compressible Euler and Navier-Stokes equations with finite-volume

discretizations on unstructured grids. Block preconditioning is used to speed up the convergence of the iterative process.

The structure of the preconditioning matrix for schemes of various orders is discussed, and a method for taking into account

boundary conditions is described. The capabilities of the approach are demonstrated by computing the low-velocity inviscid

flow over an airfoil.

discretizations on unstructured grids. Block preconditioning is used to speed up the convergence of the iterative process.

The structure of the preconditioning matrix for schemes of various orders is discussed, and a method for taking into account

boundary conditions is described. The capabilities of the approach are demonstrated by computing the low-velocity inviscid

flow over an airfoil.

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**ABSTRACT:**Optical aberrations induced by turbulent flows are a serious concern in airborne communication, imaging and optical systems because the quality of the beam degrades due to variations of the index of refraction along its path. The aero-optical aberrations produced by compressible flows are a direct consequence of the detailed physics in the flow. Time-accurate computational study of aero-optical distortions is performed based on large-eddy simulation (LES) technique because of its ability to account for the optical phase errors due to anisotropy of the flowfield and to resolve large-scale coherent structures at a reasonable computational cost. The re-normalization group (RNG) sub-grid scale model is used to account for the effect of the small turbulent eddies on the flowfield. The results of numerical simulation of turbulent flows in flat plate boundary layer, free mixing layer and free turbulent jet provide general statistics of optical distortions by examining the time-averaged intensity pattern and instantaneous flowfield. The flow-induced optical aberrations are studied for different inflow conditions. The computational tools and the results are beneficial in design and optimization of optical systems, where the control of laser beam propagation is an important problem, and coherent optical adaptive equipment and techniques based on the optical detection of light-scattering properties of the flow. Mitigation strategy is to use some sort of shear-layer control to regularize the vortex roll-up, thereby making it amenable to some form of adaptive-optic correction. - [Show abstract] [Hide abstract]

**ABSTRACT:**The features of a simplified approach to coupled thermal analysis problems as based on the integration of the energy equation for a viscous compressible gas are discussed. The gas velocity field is assumed to be frozen, and a single iteration is run to update it at each step of the coupling procedure. The equation describing the temperature distribution in a solid is discretized using the finite element method, while the Navier-Stokes equations describing the velocity and gas temperature distributions are discretized using the finite-volume method. The system of difference equations resulting from the finite-volume discretization is solved by applying a multigrid method and the generalized minimal residual method. The capabilities of the approaches developed are demonstrated by solving several model problems. The accelerations of the computational algorithm obtained with the use of the full and simplified approaches to the solution of the problem and various methods for solving the system of difference equations are compared. -
##### Article: Formulation of wall boundary conditions in turbulent flow computations on unstructured meshes

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**ABSTRACT:**Features of the formulation and numerical implementation of wall boundary conditions in turbulent flow computations on unstructured meshes are discussed. A method is proposed for implementing weak wall boundary conditions for a finite-volume discretization of the Reynolds-averaged Navier-Stokes equations on unstructured meshes. The capabilities of the approach are demonstrated in several gasdynamic simulations in comparison with the method of near-wall functions. The influence of the near-wall resolution on the accuracy of the computations is analyzed, and the grid dependence of the solution is compared in the case of the near-wall function method and weak boundary conditions.

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