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

Computational Mathematics and Mathematical Physics (Impact Factor: 0.41). 01/2009; 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.

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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.
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