A. Jameson. Multigrid Algorithms for Compressible Flow Calculations. In Proceedings of the Second European Conference on Multigrid Methods, volume 1228, pages 166--201. Spring-Verlag, 1986.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....frequency and can therefore be damped by the relaxation scheme. In the case of an explicit time stepping scheme, a significant amount of computational time can be saved through the possibility of using successively larger time steps on coarser grids without violating the stability conditions [70]. Each coarser mesh is produced by eliminating alternate points of the finer mesh, so that there exists a set of points which are common to all meshes. The cells of the fine mesh can be then combined into larger cells which form a coarser mesh. For unsteady calculations, at every physical ....

A. Jameson. Multigrid Algorithms for Compressible Flow Calculations. In Proceedings of the Second European Conference on Multigrid Methods, volume 1228, pages 166--201. Spring-Verlag, 1986.

....1 A.2.3 Time Stepping Equation A.22 is in a semi discrete form, and it must be discretized in time for numerical computations. In this work, a modified five stage Runge Kutta scheme was utilized. A complete discussion of the various aspects and choices of Runge Kutta schemes is given by Jameson [53, 52, 54, 55]. A m stage Runge Kutta scheme is as follows: l # k #tR(w l 1 The residual, R, includes contributions from the convective and dissipative terms as well as the artificial dissipation terms. In order to optimize the stability properties of the scheme, the convective and dissipative ....

A. Jameson. Multigrid algorithms for compressible flow calculations. In W. Hackbusch and U. Trottenberg, editors, Lecture Notes in Mathematics, Vol. 1228, pages 166--201. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985.

....can be greatly enhanced, particularly on stretched, large aspect ratio grids, by employing the multigrid acceleration technique. In our work, we have adopted the non linear full approximation storage scheme (FAS) 36] in conjunction with the multigrid strategy developed by Jameson [37], for the solution of the Euler equations, and extended them to solve the coupled system of mean flow and turbulence closure equations. Progress in Modeling 3D ShearFlows, F. Sotiropoulos 18 The previously described Runge Kutta algorithm (eqns. 22) is employed as the basic smoother. A ....

....respectively. To ensure that the coarse grid solution is driven by fine mesh residuals so that the reduced coarse mesh accuracy does not contaminate the accuracy of the fine mesh solution the equations solved on the coarse mesh are modified by including a forcing term 4 2h defined as follows [37]: 22, 22 r hhhhh hh TRQ RQ 4= 24) where r T is the residual restriction operator which computes a coarse grid residual by averaging the fine grid residuals over the 27 fine mesh nodes surrounding a coarse mesh node [37] The solution on the coarse mesh is then advanced in time ....

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Jameson, A., Multigrid algorithms for compressible flow calculations, MAE Report 1743, Princeton University, Princeton, NJ 08544, 1985.

....the performance of such a matrix of schemes for viscous boundary layers. Section 2 reviews the conditions for the construction of non oscillatory schemes for scalar conservation laws. Following a line adhered to in a number of works [6, 50, 25, 39] including several by the present author [18, 19, 22], it is suggested that the principle of non increasing maxima and non decreasing minima provides a convenient criterion for the design of non oscillatory schemes. This principle contains the concept of total variation diminishing (TVD) schemes for one dimensional problems, but can readily be ....

....vertex, o, say. Thus (1) is discretized as servo 1 dt (f f ) y Y ) g g ) x x ) 0 where fk = f(vk) gk = g(vk) S is the area of the polygon, and k ranges over its vertices. This may be rearranged as 11 1 1 xk = xk ) y = y ) Following, for example, References [18] and [23] this may now be reduced to a sum of differences over the edges co by noting that k Ax = A = 0. Consequently fo and go may be added to give dt (f fo) Ay (g go) Axe = 0. 20) Define the coefficient ako as (f fo)Sy (g go)SX AVCo Vk v ako Then equation (20) reduces ....

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A. Jameson. Multigrid algorithms for compressible flow calculations. In W. Hackbusch and U. Trotten- berg, editors, Lecture Notes in Mathematics, Vol. 1228, pages 166-201. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985.

....method has proved to be the most e#ective convergence acceleration procedure of all. It was originally introduced by Fedorenko [18, 19] to accelerate the convergence of solutions governed by elliptic equations. Research by Brandt [8, 9] brought the multigrid concept to its full potential. Jameson [31, 32] perfected the technique for the solution of problems governed by hyperbolic equations. In order to comprehend why the multigrid method is so successful, it is important to understand the properties of conventional iterative techniques. In order to reach equilibrium, information must be exchanged ....

A. Jameson. Multigrid algorithms for compressible flow calculations. In W. Hackbusch and U. Trottenberg, editors, Lecture Notes in Mathematics, Vol. 1228, pages 166--201. Proceedings of the 2nd European Conference on Multigrid Methods, Cologne, 1985.

.... convergence rates have been proven for elliptic operators [1, 2, 3, 4] Although no rigorous extension of this theory has emerged for problems involving a hyper1 bolic component, methods based on multigrid have proven highly effective for inviscid calculations with the Euler equations [5, 6, 7] and remain the most attractive approach for Navier Stokes calculations despite the widely observed performance breakdown in the presence of boundary layer anisotropy. Obtaining a steady state solution by timemarching the unsteady Euler or Navier Stokes equations requires elimination of ....

....space where the residual eigenvalues of high frequency modes are concentrated. Explicit multigrid solvers based on this approach represent an important schematic innovation in enabling large and complex Euler calculations to be performed as a routine part of the aerodynamic design procedure [6, 7]. However, despite the favorable convergence rates observed for Euler computations, this approach does not satisfy all the requirements for efficient multigrid performance. These shortcomings become far more evident when the approach is applied to Navier Stokes calculations. The hierarchy of ....

A. Jameson. Multigrid algorithms for compressible flow calculations. In Second European Conference on Multigrid Methods, 1985.

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Jameson A., "Multigrid Algorithms for Compressible Flow Calculation", MAE Report No.

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