Preconditioning of the Euler and Navier-Stokes equations in low-velocity flow simulation on unstructured grids
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: A new multigrid method for convection problems is presented. It is designed to overcome the problem of alignment, the flow being aligned with the grid. The technique employs semi-coarsening in several directions simultaneously and gives rise to multiple coarser grids with the same total number of points per grid-level, but with different sizes in each co-ordinate direction. The amount of work per multigrid cycle is still O(N). As an example, the method is applied to the nonlinear upwind-differenced Euler equations of gas dynamics in two dimensions. Convergence rates are estimated by two-level Fourier analysis for the linearised equations. Numerical experiments on the nonlinear equations confirm these estimates.Journal of Computational Physics 01/1989; · 2.14 Impact Factor
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ABSTRACT: In an earlier paper, an O(N) method for the computation of stationary solutions to the Euler equations of inviscid compressible gas dynamics has been described. The method is a variant of the multigrid technique and employs semi-coarsening in all co-ordinate directions simultaneously. It provides good convergence rates for first-order upwind discretisations even in the case of alignment, the flow being aligned with the grid. Here we discuss the application of this scheme to higher-order discretisations. Two-grid analysis for the linear constant-coefficient case shows that it is difficult to obtain uniformly good convergence rates for a higher-order scheme, because of waves perpendicular to stream lines. The defect correction technique suffers from the same problem. However, convergence to a point where the residual of the total error (the sum of the iteration error and the discretisation error) is of the order of the truncation error can be obtained in about seven defect correction cycles, according to estimates for the linear constant-coefficient equations. This result is explored for the nonlinear case by some illustrative numerical experiments.Journal of Computational Physics 01/1992; · 2.14 Impact Factor
- AIAA Journal 01/1995; 33(11):2050-2057. · 1.08 Impact Factor