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:**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.Computational Mathematics and Mathematical Physics 04/2013; 53(4). DOI:10.1134/S0965542513040106 · 0.79 Impact Factor -
##### 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.Computational Mathematics and Mathematical Physics 02/2014; 54(2). DOI:10.1134/S0965542514020134 · 0.79 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We have performed computational modeling of the free-convective fl ow in the gap between two coaxial cylinders on the basis of complete Navier–Stokes equations from the viewpoint of the compressible gas model. To stabilize numerical calculations of the viscous compressible gas at small Mach numbers, we used the preconditioning method based on the application of physical variables and the dual time stepping method. We have investigated the fl ow structure in the gap between the cylinders and the heat-transfer characteristics on the surface of the outer and inner cylinders at various Rayleigh numbers.Journal of Engineering Physics and Thermophysics 07/2014; 87(4):929-935. DOI:10.1007/s10891-014-1090-5

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